LSU
Mathematics

# Calendar

Time interval:   Events:

Thursday, March 20, 2003

Posted October 8, 2003

Anton Deitmar, Mathematical Sciences Department, University of Exeter
Class number asymptotics in degree 3

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Thursday, September 11, 2003

Posted September 2, 2003

3:40 pm - 4:30 pm Lockett 243

Yuri Antipov, Mathematics Department, LSU
Functional-difference equations and applications

Abstract

Thursday, September 18, 2003

Posted August 26, 2003

3:40 pm - 4:30 pm 243 Lockett Hall

Amha Lisan, Mathematics Department, LSU
Transitive flows and associated congruences and groups

Abstract

Refreshments will be served in the lounge one half hour before the talk.

Friday, September 19, 2003

Posted September 4, 2003

3:40 pm - 4:30 pm 243 Lockett Hall

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Non-commutative Analysis

Abstract

Refreshments will be served in the lounge one half hour before the talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Tuesday, September 23, 2003

Posted September 10, 2003

3:40 pm - 4:30 pm 243 Lockett Hall

Marco Schlichting, Universitat Essen, (Germany)
Hermitian K-theory and Algebraic Bott Periodicity

Refreshments will be served in the lounge one half hour before the talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Thursday, September 25, 2003

Posted August 26, 2003

3:40 pm - 4:30 pm 243 Lockett Hall

Michael M. Tom, Mathematics Department, LSU
Kadomtsev-Petviashvili and RLW-KP models

Abstract

Refreshments will be served in the lounge one half hour before the talk.

Thursday, October 30, 2003

Posted October 14, 2003

3:40 pm - 4:30 pm 243 Lockett Hall

Horst Beyer, Max Planck Institute for Gravitational Physics, Golm, Germany, and Dept. of Mathematics, LSU
On the Completeness of the Resonance Modes of the Poschl-Teller Potential

Abstract
Refreshments will be served in the lounge one half hour before the talk.

Thursday, November 20, 2003

Posted September 24, 2003

3:40 pm - 4:40 pm 243 Lockett

Yuan Wang, Florida Atlantic University
Input-to-State Stability of Nonlinear Control Systems

Abstract

Refreshments will be served in the lounge one half hour before the talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Monday, December 15, 2003

Posted December 14, 2003

2:30 pm - 3:30 pm 285 Lockett

David Levin, University of Utah
Modern Topics in Random Walks

Refreshments at 2:00 in the Keisler Lounge.

Abstract: I will survey some of my work relating to random walks: dynamical random walks and reconstruction of sceneries visited by a random walk. Dynamical random walks are easily constructed "coin tossing" analogues of infinite dimensional diffusions. We discuss the existence of times where atypical random walk behavior is seen, and give connections to the Ornstein-Uhlenbeck process on Wiener space. (Joint work with Khoshnevisan and Mendez.) Hidden Markov chains are widely applicable probabilistic models: a noisy function of an underlying stochastic process is seen, while the process itself is unobserved. We describe such models where an unknown scenery is explored by a hidden random walk, and discuss when reconstruction of this underlying scenery is possible. (Joint work with Pemantle and Peres.)

Wednesday, December 17, 2003

Posted December 17, 2003

2:30 pm - 3:30 pm

Patricia Hersh, University of Michigan
A GL_n(q) analogue of the partition lattice and discrete Morse theory for posets

Cofffe at 2:00 in the Keisler Lounge Abstract

Tuesday, January 13, 2004

Posted January 8, 2004

2:40 pm - 3:30 pm Lockett 285

Diane Maclagan, Stanford University
Toric Hilbert schemes

Abstract: Toric Hilbert schemes have broad connections to other areas of mathematics, including optimization, geometric combinatorics, algebraic geometry, and representations of finite groups and quivers. They parameterize all ideals in a a polynomial ring with the simplest possible multigraded Hilbert function. I will introduce these objects, and discuss some of the applications.

Thursday, January 22, 2004

Posted January 15, 2004

3:30 pm - 4:30 pm 285 Lockett

Scott Baldridge, Louisiana State University
Elementary Mathematics for Teachers: A mathematician's perspective

This talk describes a mathematics course, designed by mathematicians, for prospective elementary teachers. I will describe three unique features of the course: the extensive use of the Primary Mathematics books from Singapore, the idea of a teaching sequence", and the use ofteacher's solutions" in class and in homework. The course is based on a new textbook I wrote with T. Parker: Elementary Mathematics for Teachers. The goal of the textbook and the course is to present the mathematics clearly and correctly while keeping the focus on material that elementary school teachers will be addressing in their classrooms.

Refreshments in the Lounge at 3:00

Friday, January 23, 2004

Posted January 15, 2004

3:30 pm - 4:30 pm 285 Lockett

Scott Baldridge, Louisiana State University
Seiberg-Witten invariants of 4--manifolds with circle actions, with applications to symplectic topology.

Ever since the introduction of Donaldson invariants in the early 1980's, efforts to calculate diffeomorphism invariants of 4-manifolds centered upon large classes of smooth manifolds that have some additional structure. One such class of manifolds thought to have promise was 4-manifolds with effective circle actions, but the extra structure given by such manifolds turned out to be insufficient for calculating Donaldson invariants. However, it is possible to calculate their Seiberg-Witten invariants. In this talk I will give an overview of the Seiberg-Witten invariants and describe formulas for calculating the Seiberg-Witten invariant of 4-manifolds with circle actions. I will also discuss some results on the topology of symplectic 4-manifolds which follow from those calculations.

Refreshments in the Lounge at 3:00

Monday, January 26, 2004

Posted January 15, 2004

2:30 pm - 3:30 pm Lockett 237

Malabika Pramanik, University of Wisconsin - Madison

Averaging and maximal operators for curves in R^3

We consider the L^p regularity of an averaging operator over a curve in R^3 with nonvanishing curvature and torsion. We also prove related local smoothing estimates, which lead to L^p boundedness of a certain maximal function associated to these averages. The common thread underlying the proof of these results is a deep theorem of T. Wolff on cone multipliers. This is joint work with Andreas Seeger of University of Wisconsin, Madison.

Refreshments in Lounge at 2:00

Thursday, January 29, 2004

Posted January 15, 2004

3:30 pm - 4:30 pm Lockett 285

Susan Wilson, Michigan State University, College of Education
Reforming Mathematics Education; Lessons from California

Refreshments in the Lounge at 3:00

Thursday, February 5, 2004

Posted January 29, 2004

3:40 pm - 4:30 pm Lockett 285

Pramod Achar, University of Chicago
Equivariant K-theory of the unipotent variety

Abstract:
The equivariant K-theory of the unipotent variety in a complex algebraic group has two natural bases, one indexed by the set $Lambda^+$ of dominant weights, the other by the set $Omega$ of irreducible representations of centralizers of unipotent elements. Lusztig's work on cells in affine Weyl groups led him to conjecture that the change-of-basis matrix relating these two bases is upper-triangular, and that in particular there is a natural bijection between $Lambda^+$ and $Omega$. This question has been treated in the work of Bezrukavnikov, Ostrik, Xi, and others. I will discuss an approach to the problem that, in the case of $GL(n)$, results in an explicit combinatorial algorithm for computing the bijection. I will also discuss connections to the Springer correspondence, duality, and other topics.

Wednesday, February 11, 2004

Posted January 29, 2004

2:40 pm - 3:30 pm Lockett 243

Tatyana Foth, University of Michigan
Quantization, Kahler manifolds, and automorphic forms

Abstract:
I shall talk about results and problems that appear in the interplay between three subjects:
1. quantization (which can be regarded as an attempt to construct a finite-dimensional representation of the Lie algebra of smooth functions on a compact symplectic manifold with the Poisson bracket);
2. varying Kahler structure on a compact Kahler manifold with the symplectic form being kept fixed;
3. holomorphic automorphic forms on a bounded symmetric domain in C^n (for example, on the open unit ball in C^n with the Bergman metric).

Refreshments served in Keisler Lounge at 2pm.

Friday, February 13, 2004

Posted February 4, 2004

3:40 pm - 4:30 pm Lockett 285

Irina Mitrea, Cornell University
On the Spectral Radius Conjecture in Two Dimensions

Wednesday, February 18, 2004

Posted February 16, 2004

3:40 pm - 4:30 pm Lockett 285

Ruhai Zhou, Univ of North Carolina at Chapel Hill
Analysis and computations of nematic polymers

Tuesday, March 9, 2004

Posted February 2, 2004

3:40 pm - 4:30 pm Wednesday, March 10, 2004 Lockett 285

Serge Lang, Yale University Member, National Academy of Sciences
Recipient, Frank Nelson Cole Prize in Algebra
The Heat Kernel and Theta Inversion Formulas

Visit supported by Visiting Experts Program in Mathematics, Louisiana
Board of Regents LEQSF(2002-04)-ENH-TR-13

Wednesday, March 10, 2004

Posted January 30, 2004

3:40 pm - 4:30 pm Lockett 285 Originally scheduled for Thursday, February 26, 2004

Carl Mueller, University of Rochester
Properties of the Random String

Visit supported by Visiting Experts Program in Mathematics, Louisiana

Board of Regents LEQSF(2002-04)-ENH-TR-13

Thursday, March 11, 2004

Posted January 29, 2004

3:40 pm - 4:30 pm Lockett 285

Stig Larsson, University of Goteberg, Chalmers University
The finite element method for a linear stochastic parabolic partial differential equation driven by additive noise

Visit supported by Visiting Experts Program in Mathematics, Louisiana

Board of Regents LEQSF(2002-04)-ENH-TR-13

Friday, March 12, 2004

Posted March 4, 2004

3:40 pm - 4:30 pm Lockett 285

Mark Meerschaert, University of Nevada, Reno
The Fractal Calculus Project

Monday, March 15, 2004

Posted March 4, 2004

3:40 pm - 4:30 pm Lockett 285

Loukas Grafakos , University of Missouri, Columbia
Calderon's program, the bilinear Hilbert transforms, and the Carleson-Hunt theorem

Tuesday, March 16, 2004

Posted January 27, 2004

3:40 pm - 4:30 pm Lockett 285

John Willis, Cambridge University Fellow, Royal Society of London (FRS)
Bounds for the Effective Constitutive Relation of a Nonlinear Composite

Abstract:
For a nonlinear composite, a bound on its effective energy density does not induce a corresponding bound on its constitutive relation, because differentiating a bound on a function does not automatically bound its derivative. In this work, a method introduced by G.W. Milton and S.K. Serkov for bounding directly the constitutive relation is refined by employing a linear comparison material, in a similar way that Talbot and Willis introduced such a material to obtain bounds of Hashin--Shtrikman'' type for the effective energy of a nonlinear composite. The original Milton--Serkov approach produces bounds with a close relationship to the classical energy bounds, of Voigt and Reuss type. The bounds produced in the present implementation are closely related to bounds of Hashin--Shtrikman type for the composite. It is demonstrated by means of examples that the approximate constitutive relation that is obtained by differentiating the energy bound can be on the boundary of the bounding set, obtained here, for the exact constitutive relation, but a simple counterexample is presented to show that this is not always the case.

(This talk reports on joint work with D R S Talbot.)
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Thursday, March 18, 2004

Posted March 2, 2004

3:40 pm - 4:30 pm Lockett 285

Simon Gindikin, Rutgers University
Complex geometry and complex analysis on real symmetric spaces

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Tuesday, March 23, 2004

Posted March 4, 2004

3:40 pm - 4:30 pm Lockett 285

Fritz Gesztesy, University of Missouri, Columbia
On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV potential

Refreshments will be served in Keisler lounge at 3pm.

Wednesday, March 24, 2004

Posted March 3, 2004

3:40 pm - 4:30 pm Lockett 285

Alberto Setti, Universita' dell'Insubria - Como
Maximum principle on Riemannian manifolds: an overview

Refreshments will be served in Keisler lounge at 3pm.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents.
LEQSF(2002-04)-ENH-TR-13

Thursday, March 25, 2004

Posted February 11, 2004

3:30 pm - 4:30 pm Lockett Hall 285

Thomas Kerler, Ohio State University
Topological Quantum Field Theories

TQFT can be thought of as measures on topological spaces that behave nicely=functorially under the gluing of spaces. We will motivate the formalism and give an elementary construction of TQFT's starting from nothing more than the basic Seifert van-Kampen Theorem. From there we will expand on more general TQFT properties, formalisms and constructions, sketch some problems of finiteness and quantization, and present a few typical applications of TQFTs.

Refreshments will be served in the lounge one half hour before the talk.
Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Tuesday, March 30, 2004

Posted March 4, 2004

3:40 pm - 4:30 pm Lockett 285

Salah-Eldin Mohammed, Southern Illinois University, Carbondale
The Stable Manifold Theorem for Stochastic Partial Differential Equations

Wednesday, March 31, 2004

Posted March 5, 2004

3:40 pm - 4:30 pm Lockett 285

David Kirshner, Department of Curriculum and Instruction, LSU
What Ails Elementary Algebra Education: Historical, Psychological, and Philosophical Perspectives

Refreshments in Keisler Lounge at 3pm

Thursday, April 15, 2004

Posted March 23, 2004

3:30 pm - 4:30 pm

Ronald Stanke, Baylor University
Differential Operators, SL(2,R) Invariance and Special Functions

Refreshements in the Lounge one half hour befiore talk

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents.
LEQSF(2002-04)-ENH-TR-13

Thursday, April 22, 2004

Posted March 28, 2004

3:40 pm - 4:30 pm Lockett 281

Boris Rubin, The Hebrew University of Jerusalem
Selected problems of integral geometry and small denominators on the sphere

Monday, April 26, 2004

Posted April 7, 2004

3:30 pm - 4:30 pm 285 Lockett Hall

Paul Saylor, University of Illinois
What Does Radar Have to Do with Solving Sets of Linear Equations?

Tuesday, April 27, 2004

Posted March 31, 2004

3:40 pm - 4:30 pm Lockett 281

Thierry Lévy, École normale supérieure and CNRS
Two-dimensional Yang-Mills theory is almost a topological field theory

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13

Thursday, April 29, 2004

Posted March 16, 2004

3:30 pm - 4:30 pm 285 Lockett

Paulo Lima-Filho, Texas A&M
Applications of operads and ternary trees to polynomial map

Using ternary trees we build operads and use them to define a family of ideals in the (non-commutative) algebra generated by pointed ternary trees. These constructions have several applications to iterations of polynomial maps and conjectures in algebraic geometry. This is an essentially self-contained talk, accessible to a general audience and to graduate students. Refreshments will be served in the lounge one half hour before the talk.

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents.

LEQSF(2002-04)-ENH-TR-13

Thursday, May 6, 2004

Posted April 3, 2004

3:30 pm - 4:30 pm 285 Lockett Hall

Milton C. Lopes Filho, Penn State University and UNICAMP, Brazil
Open problems on mathematical hydrodynamics

Abstract: Mathematical hydrodynamics is primarily concerned with the behavior of solutions of the incompressible Euler and Navier-Stokes equations. These nonlinear systems of PDEs have a rich mathematical structure that keeps hydrodynamics a topic of current interest in mathematical research. One illustration of the cogency of this topic is the choice of the singularity problem for the Navier-Stokes equations as one of the seven Millenium Prize Problems. Problems in the field of mathematical hydrodynamics often reduce to proving that solutions of the incompressible flow equations behave as actual fluids are known to behave. In this talk we will examine a few instances where the known behavior of real fluids leads to open problems on the behavior of solutions of the incompressible flow equations, exploring the power, and the limitations, of modern analytic techniques used in the treatment of these problems.

Refreshments will be served in the lounge one half hour before the talk. Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents. LEQSF(2002-04)-ENH-TR-13

Friday, May 14, 2004

Posted May 13, 2004

3:30 pm - 4:30 pm Lockett 285

Cun-Quan Zhang, West Virginia University
Some Results about Integer Flows

Refreshments in Keisler Lounge at 3pm

Thursday, September 23, 2004

Posted September 17, 2004

3:30 pm - 4:30 pm Lockett 277

Daniel Sage, Mathematics Department, LSU
Group and quantum group actions on algebras and composite materials

Thursday, September 30, 2004

Posted September 23, 2004

3:30 am - 4:30 am Lockett 277

Ricardo Estrada, Mathematics Department, LSU
On the regularization of generalized functions

Tuesday, October 5, 2004

Posted September 30, 2004

3:30 pm - 4:30 pm Lockett 239

Mark Davidson, Mathematics Department, LSU
Generating functions associated to Highest Weight Representations

Thursday, October 28, 2004

Posted October 20, 2004

3:40 pm - 4:30 pm Lockett 277

Fernando Rodriguez-Villegas, University of Texas at Austin
The Many Aspects of Mahler's Measure

Visit supported by Visiting Experts Program in Mathematics, Louisiana Board of Regents LEQSF(2002-04)-ENH-TR-13 Refreshments will be served in the lounge at 3pm.

Wednesday, December 8, 2004

Posted November 29, 2004

3:40 pm - 4:30 pm 277 Lockett

Christopher Leininger, Columbia University Candidate for Assistant Professor Position in Topology
Teichmuller disks in geometry and topology

Refreshments in Keisler Lounge at 3:00 PM

Tuesday, January 18, 2005

Posted December 13, 2004

3:40 pm Lockett 285

Selim Esedoglu, UCLA Candidate for Assistant Professor Position in Applied Math
Threshold dynamics for the piecewise constant Mumford-Shah

Wednesday, January 19, 2005

Posted January 5, 2005

3:40 pm Lockett 285

Burak Aksoylu, University of Texas at Austin, Institute for Computational Eng. and Science Candidate for Assistant Professor Position in Scientific Computation
Local refinement and single/multi level preconditioning with applications in biophysics, computer graphics, and geosciences

Tuesday, January 25, 2005

Posted December 13, 2004

3:40 pm Lockett 285 Originally scheduled for 3:40 pm, Thursday, January 20, 2005

Valeriy Slastikov, Carnegie mellon University Candidate for Assistant Professor Position in Applied Math
Geometrically Constrained Walls

Friday, January 28, 2005

Posted January 24, 2005

1:40 pm Lockett 138

Tara Brendle, Mathematics Department, Cornell University Candidate for Assistant Professor Position in Topology
Mapping class groups and complexes of curves

Posted January 24, 2005

3:40 pm Lockett 285

Brendan Owens, Mathematics Department, Cornell University Candidate for Assistant Professor Position in Topology
Four-manifolds with prescribed boundary and applications to knot theory

Tuesday, February 1, 2005

Posted January 21, 2005

3:40 pm Lockett 285

Masako(Marta) Asaeda, Mathematics Department, University of Iowa Candidate for Assistant Professor Position in Topology
Generalizations of Khovanov homology

Wednesday, February 2, 2005

Posted January 26, 2005

3:40 pm Lockett 285

Hongyu He, Mathematics Department, LSU
Tensor Products of Oscillator Representations

Friday, February 11, 2005

Posted January 26, 2005

3:40 pm Lockett 285

Ai-Ko Liu, U. C. Berkeley, Mathematics Candidate for Assistant Professor in Geometric Analysis
Cosmic String, Family Seiberg-Witten theory and Harvey-Moore Conjecture

Tuesday, February 15, 2005

Posted January 31, 2005

3:40 pm Lockett 285

Justin Sawon, Department of Mathematics, SUNY at Stony Brook Candidate for Assistant Professor in Topology
Derived equivalence of algebraic varieties

Wednesday, February 16, 2005

Posted January 31, 2005

3:40 pm Lockett 285

Yann Rollin, MIT, Department of Mathematics Candidate for Assistant Professor in Geometric Analysis
Construction of Kaehler surfaces with constant scalar curvature

Tuesday, February 22, 2005

Posted February 16, 2005

3:30 pm - 4:30 pm Lockett 285

Leticia Barchini, Oklahoma State University at Stillwater
Positivity of Zeta distributions and small representations

Abstract: We study positivity of zeta distributions associated to noneuclidean Jordan algebras. The values of the complex parameter s for which the distributions are positive is determined. A theory analogous to the classical theory of Riesz distributions and Wallach set is developed. We claculate the distributions when they are positive. For each value of s for which the zeta distribution is positive we build a Hilbert space. These Hilbert spaces are representations spaces for the conformal groups of the Jordan algebras involved. In this way we build an explicit family of small (non holomorphic) representations.

Thursday, February 24, 2005

Posted February 21, 2005

2:00 pm - 2:50 pm Lockett 277

Stephen(Steve) Bryson, NASA Ames Research Center Candidate for Assistant Professor Position in Scientific Computation
Central Methods for Balance Laws

Thursday, March 3, 2005

Posted February 23, 2005

3:40 pm Lockett 285

Yaniv Almog, Department of Mathematics/ Technion-I.I.T. Candidate for Assistant Professor Position in Applied Math
Abrikosov lattices in finite domain

Monday, March 7, 2005

Posted February 23, 2005

3:40 pm Lockett 285

Petr Plechak, Mathematics Institute, University of Warwick Candidate for Associate Professor Position in Scientific Computation
Approximation and coarse-graining of stochastic lattice systems

Tuesday, March 8, 2005

Posted March 1, 2005

3:40 pm - 4:30 pm Lockett 285

Brian Hall, University of Notre Dame
The range of the heat operator

Abstract: I will consider the heat operator both on Euclidean space and on certain symmetric manifolds such as spheres and hyperbolic spaces. I will begin by reviewing the heat equation itself, which describes how temperature distributions evolve in time. Then I will consider the following question: What class of functions does one obtain by taking an arbitrary initial temperature distribution and then running the heat equation for some fixed time t? The heat equation is very smoothing: the diffusion of heat smoothes out any rough edges in the initial temperature distribtion. Thus the functions obtained must be very nice ones and I will characterize them in terms of their analyticity properties. My talk will follow a recent reprint, available at www.arxiv.org/abs/math.DG/0409308.

Thursday, March 31, 2005

Posted February 22, 2005

3:30 pm - 4:30 pm Lockett 285

Alexander Figotin, University of Californina at Irvine
Nonlinear dispersive media

We study the basic properties of the Maxwell equations for nonlinear inhomogeneous media. Assuming the classical nonlinear optics representation for the nonlinear polarization as a power series, we show that the solution exists and is unique in an appropriate space if the excitation current is not too large. The solution to the nonlinear Maxwell equations is represented as a power series in terms of the solution of the corresponding linear Maxwell equations. This representation holds at least for the time period inversely proportional to the appropriate norm of the solution to the linear Maxwell equation. We derive recursive formulas for the terms of the power series for the solution including an explicit formula for the first significant term attributed to the nonlinearity. Coffee will be served in the Keisler Lounge at 3:00pm

Monday, April 11, 2005

Posted March 28, 2005

3:40 am - 4:30 am Lockett 285

Xiao-Song Lin, University of California Riverside
A folding problem of polygonal arcs in 3-space

Thursday, April 14, 2005

Posted March 1, 2005

3:40 pm - 4:30 pm Lockett 241

Dror Bar-Natan, University of Toronto
Local Khovanov Homology

Abstract

Visit supported by Visiting Experts Program in Mathematics, Louisiana
Board of Regents LEQSF(2002-04)-ENH-TR-13

Monday, April 18, 2005

Posted April 15, 2005

11:00 am Coates 202

Martin Olbrich, Universität Göttingen
Automorphic distributions and dynamical zeta functions

Thursday, April 28, 2005

Posted March 15, 2005

11:00 am - 12:00 pm 104 Hill Memorial Library Originally scheduled for 3:40 pmTuesday, April 12, 2005

Roger Howe, Yale University
More than Mathematics for Teaching

Abstract: There has been substantial agreement among
professionals concerned with mathematics education
that the mathematical skills of the teaching corps needs
to be substantially upgraded. This is an urgent project
which will require huge effort. At the same time we
work on this, however, we should not lose sight of the
fact that there are certain jobs, in particular,
mathematics supervisor, which require substantially higher
levels of expertise than classroom teaching. Furthermore,
the system as a whole needs means to improve its understanding
of both mathematics teaching practice and curriculum.
This talk will discuss these issues, and some possible means for

Thursday, September 29, 2005

Posted September 2, 2005

3:40 pm - 4:30 pm Lockett 235

Jacob Rubinstein, Indiana University
The weighted least action principle

Abstract

Thursday, November 10, 2005

Posted September 28, 2005

3:40 pm - 4:30 pm Lockett 235 Originally scheduled for 3:40 pm, Thursday, October 20, 2005

Richard Anderson, Louisiana State University (Emeritus) Emeritus Boyd Professor.
My Three Lives in Mathematics

Abstract

Refreshments will be served in the James E. Keisler Lounge one half hour before the talk.

Monday, December 12, 2005

Posted November 30, 2005

3:40 pm - 4:30 pm Lockett 285

Changyou Wang, University of Kentucky Candidate for an Associate/Full Professor Position in Partial Differential Equations
Calculus of variations in L-infinity and Aronsson's equation

ABSTRACT: In this talk, I will discuss the basic issues for L-infinity variational problems, where one considers minimization problem of the supernorm functional: $$F(u,Omega)=esssup H(x,u(x),nabla u(x)), uin W^{1,infty}(Omega).$$ We will survey some recent developments on: (1) the existence of absolute minimizers (AM's), (2) the PDE characterization of AMs (i.e. Aronsson's equation or AE), (3) the relationship between AM and AE, and (4) regularity and uniqueness of AE. We will also discuss its connection with image interpolation, random game theory.

Wednesday, February 1, 2006

Posted January 13, 2006

3:40 pm - 4:30 pm Lockett 284

David Damanik, California Institue of Technology Candidate for Full Professor Position
Structures of intermediate complexity and quantum dynamics

Abstract: We discuss the spreading properties of quantum particles in structures of intermediate complexity. Examples of interest include quasicrystals. We carry out a complete analysis for the Fibonacci Hamiltonian, which is the most prominent object in the mathematics and physics literature on quasicrystals.

Tuesday, February 7, 2006

Posted February 3, 2006

3:00 pm - 4:00 pm Lockett 284

Dana Scott, Carnegie Mellon University
Parametric Sets and Virtual Classes

Wednesday, February 22, 2006

Posted February 15, 2006

3:30 pm - 4:30 pm Lockett 284

Dorin Dutkay, Rutgers University
Wavelets and self-similarity

In the past twenty years the theory of wavelets has proved to be extremely successful, with important applications to image compression and signal processing. The theory involves the consctruction of orthonormal bases in euclidian spaces generated by translations and dilations. A key feature of these consctructions is the property of self-similarity. We exploit this property and, using operator algebra methods, we offer a wider perspective on the subject. We show how techniques from the theory of wavelets can be used in many other contexts such as fractals, dynamical systems, or endomorphisms of von Neumann algebras. Thus, we can construct rich multiresolution structures with scaling functions and wavelets on fractals, solenoids, super-wavelets for Hilbert spaces containing L^2(R), or harmonic bases on fractal measures.

Thursday, February 23, 2006

Posted February 17, 2006

11:40 am - 12:30 pm Johnston 338

Susanne Brenner, Department of Mathematics, University of South Carolina
Fast Solvers for $C^0$ Interior Penalty Methods

In this talk we will discuss fast solvers for $C^0$ interior penalty
methods for fourth order elliptic boundary value problems. We will
give a brief introduction to $C^0$ interior penalty methods, and
present convergence results for the V-cycle, W-cycle and F-cycle
multigrid algorithms, and also condition number estimates for
two-level additive Schwarz preconditioners. Numerical results will
also be reported.

Posted February 15, 2006

1:40 pm - 2:30 pm Lockett 16

Dave Larson, Texas A&M
Wavelet Sets and Interpolation

A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or "system", of unitary operators defined in terms of translation and dilation operations. We will begin by describing an operator-interpolation approach to wavelet theory using the local commutant of a unitary system that was developed by the speaker and his collaborators a few years ago. This is really an abstract application of the theory of operator algebras, mainly von Neumann algebras, to wavelet theory. The concrete applications of oeprator-interpolation to wavelet theory include results obtained and partially published results, and some brand new results, that are due to this speaker and his former and current students, and other collaborators.

Posted February 16, 2006

3:40 pm - 4:30 pm Lockett 284

Chris Hruska, University of Chicago Candidate for an Assistant Professor Position in Topology
Nonpositively curved spaces with isolated flats

Abstract: In the 1980s Gromov popularized the study of finitely generated groups using geometric techniques. He introduced and popularized notions of negative and nonpositive curvature in group theory, which have been highly influential in shaping the field of geometric group theory over the last two decades. The theory of negatively curved groups is extremely rich and exhibits many strong stability properties. On the other hand, the theory of nonpositively curved groups is much more delicate and less understood. In my thesis, I introduced the class of nonpositively curved groups with isolated flats''. These groups occur naturally throughout group theory and low-dimensional topology and can be considered as the simplest nontrivial generalization of a negatively curved group. They have many properties in common with negatively curved groups. In particular, in joint work with Bruce Kleiner, I have shown that such a group is relatively hyperbolic with respect to virtually abelian subgroups.

Friday, February 24, 2006

Posted February 16, 2006

1:40 pm - 2:30 pm Lockett 16

(Jennifer)Suzanne Hruska, Indiana University Candidate for an Assistant Professor Position in Analysis
The Dynamics of Polynomial Skew Products of C^2''

Our goal is to develop and use rigorous computer investigations to study the dynamics of polynomial skew products of C^2; i.e., maps of the form f(z,w) = (p(z), q(z,w)), where p and q are polynomials of the same degree d >= 2. The skew products we are most interested in studying are those maps which are Axiom A. Such maps have the simplest'' chaotic dynamics, and stability under small perturbation, thus are amenable to computer investigation. In this talk, we will describe a new class of skew products with interesting dynamics, and sketch how we have proven using rigorous computer techniques that sample maps from this class are Axiom A. This leads us to conjecture that all (or nearly all) maps in this class are Axiom A.

Posted February 17, 2006

3:40 pm - 4:30 pm Lockett 284

Li-yeng Sung, University of South Carolina Candidate for Possible Senior Professor Position
Fokas Transforms

Just as initial value problems for evolution partial differential equations in one spatial variable can be solved by means of the Fourier transform on the full-line, initial-boundary value problems on the half-line can be solved using Fokas transforms. In this talk we will present unified derivations of these transforms and discuss their applications to linear and nonlinear partial differential equations.

Friday, March 3, 2006

Posted February 23, 2006

1:40 pm - 2:30 pm Lockett 277

Olga Plamenevskaya, Massachusetts Institute of Technology Candidate for Assistant Professor Position in Topology
Heegaard Floer theory, knots, and contact structures

Abstract: Heegaard Floer theory is one of the most significant recent developments in low-dimensional topology. Reminiscent of gauge theory, it provides powerful invariants for 3-manifolds. Although defined via holomorphic disks, these 3-manifold invariants have an unexpected connection to combinatorial knot invariants developed by Khovanov. I will outline the construction of Heegaard Floer and Khovanov theories, as well as their relation (due to Ozsvath and Szabo). Then, I will expand these results to the world of contact topology, providing a new invariant for transversal knots, and bringing the correspondence between the two theories to a new level.

Posted February 23, 2006

3:40 pm - 4:30 pm Lockett 284

Alexander Retakh, University of Texas at Arlington Candidate for Assistant Professor Position in Algebra
Structure Theory and Representations of Conformal Algebras

The last several decades saw a great deal of interaction between representation theory and modern mathematical physics. The search for rigorous algebraic formalism in areas such as string theory and conformal field theory led Kac and others to the concept of a conformal algebra. Apart from their physical applications, conformal algebras also turned out to be extremely useful in the study of infinite-dimensional Lie algebras. I will define conformal algebras, explain their relation to vertex algebras and superconformal algebras of string theory, the connection to Hamiltonian formalism in calculus of variations, and describe recent progress and conjectures in the field.

Friday, March 10, 2006

Posted February 27, 2006

3:40 pm - 4:30 pm Lockett 284

Chris Larsen, WPI and California Institute of Technology
Epsilon Stability - A new tool for studying local minimizers

Friday, March 17, 2006

Posted March 17, 2006

3:40 pm - 4:30 pm Lockett 284

Leonid Berlyand, Department of Mathematics, Penn State University
The discrete network approximation and asymptotic fictitious fluid approach in modeling of highly packed composites

Posted March 17, 2006

3:40 pm - 4:30 pm Lockett 284

Achim Jung, Department of Computer Science, University of Birmingham, England
Semantic domains, or the curious incapability of mathematics in computer science

Abstract: In the mid-60s, Christopher Strachey and others begun a programme of describing the meaning of computer programs in a mathematical style. The approach is known as denotational semantics. From the beginning, Strachey was aware that set theory is not a good basis for such an endeavour, but it was not until Dana Scott developed his domain theory several years later that there was any mathematical basis at all. In this talk, I will try to explain why sets - without further structure - do not reflect well the realities of computing, and I will try to motivate why the domains of Scott, which carry an order and a topology, do a better job. There are several further computational phenomena which required Scott to restrict the concept of domain even further, but once this is done, a fairly pleasing and flexible semantic universe is obtained. In the spirit of this lecture, I will not dwell too much on the successes that domain theory has had in modelling computation, but rather present those phenomena which have resisted being incorporated into the model. One issue that is still not completely understood is the treatment of exact real numbers. On the one hand, real numbers seem ideally suited for a topological model but recent work by Escardo, Hofmann, and Streicher suggests that there is an inherent conflict between efficiency of the programming language and faithfulness to the mathematical concept.

Tuesday, March 21, 2006

Posted March 21, 2006

3:40 pm - 4:30 pm Lockett 284

Achim Jung, Department of Computer Science, University of Birmingham, England
Semantic domains, or the curious inapplicability of mathematics in computer science

ABSTRACT: In the mid-60s, Christopher Strachey and others begun a
programme of describing the meaning of computer programs in a mathematical
style. The approach is known as denotational semantics. From the
beginning, Strachey was aware that set theory is not a good basis for such
an endeavour, but it was not until Dana Scott developed his domain
theory several years later that there was any mathematical basis at all.

In this talk, I will try to explain why sets - without further structure -
do not reflect well the realities of computing, and I will try to motivate
why domains of Scott, which carry an order and a topology, do a better job.
There are several further computational phenomena which required Scott to
restrict the concept of domain even further, but once this is done, a
fairly pleasing and flexible semantic universe is obtained.

In the spirit of this lecture, I will not dwell too much on the successes
that domain theory has had in modelling computation, but rather present
those phenomena which have resisted being incorporated into the model. One
issue that is still not completely understood is the treatment of exact
real numbers. On the one hand, real numbers seem ideally suited for a
topological model but recent work by Escardo, Hofmann, and Streicher
suggests that there is an inherent conflict between efficiency of the
programming language and faithfulness to the mathematical concept.

Monday, March 27, 2006

Posted March 9, 2006

3:40 pm - 4:30 pm Johnston 338

Qian-Yong Chen, University of Minnesota Candidate for Assistant Professor Position
A new basis for spectral methods

Abstract: The spectral methods have been very successful in many applications, such as weather prediction, seismic imaging and etc. The main reason for their success is the exponential accuracy: For smooth problems on simple domains, spectral methods can achieve 10 digits accuracy, compared to 2 ~ 3 digits for finite difference or finite element methods with similar computational cost. However, there are still two issues with the Legendre/Chebyshev polynomials based spectral methods for non-periodic problems: the time-step size and the number of points needed to resolve a wave. In this talk, I address this two issues by using a new basis, the prolate spheroidal wave functions (PSWFs), for spectral methods. The relevant approximation theory will be covered. The advantage of the new basis over Legendre/Chebyshev polynomials will be showed for marginally resolved broadband solutions.

Friday, March 31, 2006

Posted March 24, 2006

9:00 am - 10:00 am 338 Johnston Hall/CCT

Christopher King, Northeastern University
Mathematical problems in quantum information theory

Abstract

Thursday, April 20, 2006

Posted April 10, 2006

3:40 pm - 4:30 pm Lockett 284

Atle Hahn, University of Bonn and LSU
Towards a path integral derivation of 3-manifold quantum invariants

Abstract: The study of the heuristic Chern-Simons path integral by E. Witten inspired (at least) two general approaches to quantum topology. Firstly, the perturbative approach based on the CS path integral in the Landau gauge and, secondly, the quantum group approach by Reshetikhin and Turaev. While for the first approach the relation to the CS path integral is obvious for the second approach it is not. In particular, it is not clear if and how one can derive the relevant R-matrices or quantum 6j-symbols directly from the CS path integral. In my talk, I will sketch a strategy that should lead to a clarification of this issue in the special case where the base manifold is of product form. This strategy is based on the torus gauge fixing procedure introduced by Blau and Thompson for the study of the partition function of CS models. I will show that the formulas of Blau and Thompson can be generalized to Wilson lines and that the evaluation of the expectation values of these Wilson lines leads to the same state sum expressions in terms of which shadow invariant of Turaev is defined. Finally, I will sketch how one can obtain a rigorous realization of the path integral expressions appearing in this treatment.

Thursday, April 27, 2006

Posted April 21, 2006

3:40 pm - 4:30 pm Lockett 284

Tomasz Przebinda, University of Oklahoma
Invariant Eigen-Distributions and Howe's Correspondence

Abstract: The notions of a group reduction, a character and an invariant eigen distribution play a crucial role in Harmonic Analysis on a Real Reductive Group. The classical groups may be organized in pairs. This leads to a correspondence of representations, which is compatible with Capelli identities. We shall explain a recent microlocal construction of invariant eigen distributions which is also compatible with Capelli identities. The hope is that this construction explains the behavior of the characters under Howe's correspondence.

Thursday, May 4, 2006

Posted April 19, 2006

3:40 pm 284 Lockett

Franco Rampazzo, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova Professor of Mathematical Analysis
Commutators of Flows of Non-Smooth Vector Fields

Professor Rampazzo's visit is sponsored by the Louisiana Board of Regents Grant "Enhancing Control Theory at LSU". This is one of two talks the speaker will give at LSU during May 2006. For abstracts of both talks, click here.

Thursday, September 14, 2006

Posted September 1, 2006

3:40 pm - 4:30 pm Locket 285

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Hilbert Tensor Algebras and Stochastic Differential Equations

Thursday, September 21, 2006

Posted September 13, 2006

3:40 pm - 4:30 pm Lockett 285

Michael Malisoff, LSU
Lyapunov Functions, Stabilization, and Engineering Applications

Thursday, October 19, 2006

Posted October 5, 2006

3:40 pm - 4:30 pm Lockett 285

Habib Ouerdiane, University of Tunis
Infinite Dimensional Complex Analysis and Application to Probability

There will be coffee and cookies in the lounge at 3:00.

Thursday, October 26, 2006

Posted October 4, 2006

3:40 pm - 4:30 pm Lockett 285

Sarada Rajeev, Department of Physics and Astronomy, University of Rochester
The Stochastic Geometry of Two Dimensional Turbulence

Abstract

Thursday, November 2, 2006

Posted September 26, 2006

3:40 pm - 4:30 pm Lockett 285

Darren Crowdy, Imperial College London and MIT
Vortex motion in complex domains: new theoretical perspectives

Here is the abstract. There will be coffee and cookies in the lounge at 3:00.

Thursday, November 9, 2006

Posted October 5, 2006

3:40 pm - 4:30 pm Lockett 285

Paul Kirk, Indiana University
The geography of 4-manifolds with specified fundamental group

There will be coffee and cookies in the lounge at 3:00.

Tuesday, November 14, 2006

Posted October 4, 2006

3:40 pm - 4:30 pm Lockett 285

Thierry Lévy, École normale supérieure and CNRS
Combinatorial aspects of the heat kernel measure on the unitary group

Abstract

Thursday, November 16, 2006

Posted October 20, 2006

3:40 pm - 4:30 pm Lockett 285

Larry Gerstein, University of California at Santa Barbara
Quadratic forms: classification and other problems

Here is the abstract. There will be coffee and cookies in the lounge at 3:00.

Friday, November 17, 2006

Posted November 2, 2006

3:40 pm - 4:30 pm 109 Nicholson

John Baez, Univeristy of California at Riverside
Higher Gauge Theory

This is a joint Mathematics and Physics & Astronomy Event.
Abstract

Wednesday, November 29, 2006

Posted October 5, 2006

3:40 pm - 4:30 pm Lockett 235

Samuel M. Rankin, Director, American Mathematical Society Washington Office
Activities of the American Mathematical Society's Washington Office

There will be coffee and cookies in the lounge at 3:00.

Thursday, November 30, 2006

Posted September 29, 2006

3:40 pm - 4:30 pm Lockett 285

Phuc Nguyen, Purdue University
Nonlinear equations with power source terms and measure data

Here is the abstract. There will be coffee and cookies in the lounge at 3:00.

Thursday, January 18, 2007

Posted January 14, 2007

3:40 pm - 4:30 pm Lockett 277

Carlos A. Berenstein, University of Maryland
Internet Tomography

Abstract: The problem to be discussed is how to detect as early as possible an attack on a network by saturation. There will be coffee and cookies in the lounge at 3:00.

Thursday, January 25, 2007

Posted January 15, 2007

3:40 pm - 4:30 pm Lockett 277

Jan Dijkstra, Vrije Universiteit Amsterdam
On sets with convex shadows

Here is the abstract. There will be coffee and cookies in the lounge at 3:00.

Wednesday, January 31, 2007

Posted January 18, 2007

3:40 pm - 4:30 pm Lockett 285

Kariane Calta, Cornell University Candidate for Assistant Professor Position
Billiards, translation surfaces and associated dynamical systems

Abstract:
In this talk I will discuss some of the basic notions relevant to the
study of translation surfaces and provide several interesting
examples of such surfaces, including those that arise from billiard
tables. I will focus
on the dynamics of the geodesic flow on an individual
surface and the related dynamics of the action of SL(2,R) on the moduli
space of translation surfaces. I will also discuss recent advances in this
field, including some of my own results and their relationship to the work
of a number of other authors.

Friday, February 2, 2007

Posted January 26, 2007

3:40 pm - 4:30 pm Lockett 285

Ioan Bejenaru, Univ of California, Los Angeles Candidate for Assistant Professor Position
Local and global solutions for Schroedinger Maps

Abstract: We introduce the Schroedinger Maps which can be thought as free solutions of the geometric Schroedinger equation. More exactly, while the classical Schroedinger equation is written for functions taking values in $\mathhb{C}$ (complex plane), the range of a Schroedinger Map is a manifold (with a special structure). We explain the importance of these Maps and what are the fundamental aspects one would like to understand about them. Then we focus on the particular case when the target manifold is $\mathbb{S}^2$ (the two dimensional sphere) and review the most recent results along with our contribution to the field.

Monday, February 5, 2007

Posted January 29, 2007

3:40 pm - 4:30 pm Lockett 285

Mahta Khosravi, Institute for Advanced Study, Princeton, NJ Candidate for Assistant Professor Position
Spectral Asymptotics on Heisenberg Manifolds

abstract: Let R(t) be the error term in Weyl's law for (2n+1)-dimensional Heisenberg manifolds. Based on the Petridis-Toth conjecture R(t)=O_delta(t^{n-1/4+delta}). We discuss new pointwise and moment results that provide evidence for this conjecture in three dimensions and a proof for it in higher dimensions. The methods used also allow a proof of a new fifth moment result in the case of the Dirichelet Divisor problem.

Monday, February 12, 2007

Posted January 22, 2007

3:40 pm - 4:30 pm Lockett 285

Milen Yakimov, University of California, Santa Barbara
Poisson structures on flag varieties

Abstract: The geometry of Poisson structures originating from Lie theory found numerous applications in representation theory, ring theory, and dynamical systems. The linear Poisson structure on the dual of a Lie algebra provides the setting for the orbit method of Kirillov, Kostant, and Dixmier for the study of the unitary duals of Lie groups and the spectra of universal enveloping algebras. In this talk we will describe in detail the geometry of a class of Poisson structures on complex flag varieties and some of their relations to combinatorics (Schubert cells and their Deodhar partitions, cluster algebras, total positivity, the Springer and the Lusztig partitions of wonderful compactifications), ring theory (spectra of algebras of quantum matrices and other quantized algebras), integrable systems (Kogan-Zelevinsky systems). In the special case of hermitian symmetric spaces of compact type, these Poisson structures further elucidate the works of Wolf, Richardson, R\"ohrhle, and Steinberg on the structure of the orbits of certain Levi factors.

Wednesday, February 14, 2007

Posted January 29, 2007

3:40 pm - 4:30 pm Lockett 285

Christian Haesemeyer, University of Illinois, Urbana-Champaign Candidate for Assistant Professor Position
On the algebraic K-theory of singularities

Abstract: Algebraic K-theory is a highly complicated invariant of algebraic varieties and rings, encoding arithmetic, geometric and algebraic information. In this talk, I will try to explain these different notions and give some idea as to how to isolate geometric from algebraic information in the case of singularities.

Friday, February 23, 2007

Posted February 14, 2007

3:40 pm - 4:30 pm Lockett 285

Milen Yakimov, University of California, Santa Barbara
Poisson structures on flag varieties

Abstract: The geometry of Poisson structures originating from Lie theory found numerous applications in representation theory, ring theory, and dynamical systems. The linear Poisson structure on the dual of a Lie algebra provides the setting for the orbit method of Kirillov, Kostant, and Dixmier for the study of the unitary duals of Lie groups and the spectra of universal enveloping algebras. In this talk we will describe in detail the geometry of a class of Poisson structures on complex flag varieties and some of their relations to combinatorics (Schubert cells and their Deodhar partitions, cluster algebras, total positivity, the Springer and the Lusztig partitions of wonderful compactifications), ring theory (spectra of algebras of quantum matrices and other quantized algebras), integrable systems (Kogan-Zelevinsky systems). In the special case of hermitian symmetric spaces of compact type, these Poisson structures further elucidate the works of Wolf, Richardson, R\"ohrhle, and Steinberg on the structure of the orbits of certain Levi factors.

Monday, February 26, 2007

Posted January 5, 2007

3:40 pm - 4:30 pm Lockett 277

Max Karoubi, University of Paris 7
Twisted K-theory, old and new

Abstract: Twisted K-theory has its origins in the author's PhD thesis [K1] and in the paper of P. Donovan and the author about 37 years ago. The objective of the lecture is to revisit the subject in the light of new developments inspired by Mathematical Physics. See for instance E. Witten Arxiv hep-th/9810188, J. Rosenberg. and M.F. Atiyah-G. Segal ArXiv math/0407054. The unifiying theme is the notion of K-theory of graded Banach algebras, already present in [K1], from which most of the new theorems in twisted K-theory are derived. Some explicit computations are also given in the equivariant case, related to previous known results. (see http://www.math.jussieu.fr/~karoubi/ or ArXiv mathKT/0701789 for more details)

There will be coffee and cookies in the lounge at 3:00.

Thursday, March 8, 2007

Posted February 14, 2007

3:40 pm - 4:30 pm Lockett 285

Michael Otto, University of Arizona
The moment map in symplectic geometry and elsewhere

Abstract: The moment map is a central object of study in symplectic geometry. It also appears (in disguise) in several other branches of mathematics, such as linear algebra, classical mechanics, representation theory of Lie groups etc. This talk is intended to give an overview over some of its most interesting properties, most notably several convexity results and formulas of Duistermaat-Heckman type.

There will be coffee and cookies in the lounge at 3:00.

Thursday, April 19, 2007

Posted April 11, 2007

3:40 pm - 4:30 pm Lockett 277

Kevin Knudson, Mississippi State University
Algorithms in discrete Morse theory

Abstract: Discrete Morse theory was developed by Robin Forman to
provide a combinatorial analogue, for simplicial complexes, of classical
smooth Morse theory on manifolds. Constructing efficient discrete Morse
functions is a nontrivial task. In this talk, I will present an
algorithm that begins with a function h defined on the vertices of a
complex K and extends it to a discrete Morse function on the entire
complex so that the resulting discrete gradient field mirrors the large
scale behavior of h. This has applications to the analysis of point
cloud data sets and several examples will be given. No prior knowledge
of Morse theory (discrete or smooth) will be assumed.

There will be coffee and cookies in the lounge at 3:00.

Wednesday, May 2, 2007

Posted March 30, 2007

3:40 pm - 4:30 pm Lockett 285

William Velez, The University of Arizona
Increasing the number of mathematics majors

Abstract

In the late 1980?s I began my efforts to increase the success rate of minorities in first semester calculus. The interventions that I devised were very time consuming and as the number of minority students increased, I could not manage that kind of effort. I developed my Calculus Minority Advising Program in an effort to meet with scores of minority students each semester. This program consists of a twenty-minute meeting with each student at the beginning of each semester. These meetings with students eventually transformed my own attitude about the importance of mathematics in their undergraduate curriculum.

I took over the position of Associate Head for Undergraduate Affairs in the department four years ago. I set a very modest goal for myself: to double the number of mathematics majors. With almost 500 mathematics majors I have reached that goal. I think the next doubling is going to be much harder to achieve. My work with minority students provided me with the tools to accept this new challenge of working with all students.

This talk will describe my own efforts to encourage ALL of our students that a mathematics major, or adding mathematics as a second major, is a great career choice.

Thursday, May 3, 2007

Posted April 23, 2007

3:40 pm Lockett 285

Raul Quiroga, Centro de Investigacion en Matematicas (cimat)
Actions of Noncompact Simple Lie Groups on Pseudo Riemannian Manifolds

Let G be a noncompact simple Lie group acting on a compact manifold M, and suppose that the G-action has a dense orbit and preserves a pseudoRiemannian metric. A general conjecture of R. Zimmer states that, for this geometric/dynamical setup, M is essentially a coset space of a semisimple Lie group H containing G. In this talk we will discuss some geometric conditions on the G-action on M that ensure the conclusion of Zimmer's conjecture.

Tuesday, October 16, 2007

Posted September 19, 2007

10:00 am Johnston Hall 338

Doug Arnold, Institute for Mathematics and its Applications, Minneapolis Director
The Institute for Mathematics and its Applications

Abstract: The Institute for Mathematics and its Applications (IMA) in Minneapolis is a leading research center, founded by the National Science Foundation in 1982. The primary mission of the IMA is to increase the impact of mathematics by fostering interdisciplinary research linking mathematics with important scientific and technological problems from other disciplines, industry, and society. Through a variety of programs, it provides opportunities for scientists, mathematicians, and engineers from academia and government labs and industry to make contact and interact with each other, to learn about new developments, and to stimulate the study of interesting and relevant problems and their solution. In this informal presentation the director of the IMA will discuss IMA operations, upcoming programs, and outcomes, in order to promote participation and gather input from LSU researchers.

Thursday, October 18, 2007

Posted September 28, 2007

3:40 pm - 4:30 pm Lockett 285

John Etnyre, Georgia Institute of Technology
Invariants of embeddings via contact geometry

Abstract: I will describe a method to define, hopefully new, invariants of any embedded submanifold of Euclidean space. To define this invariant we will need to take an excursion into the realm of contact geometry and a recent generalization of Floer homology called contact homology. More specifically, after recalling various notions from contact geometry, I will show how to associate a Lagrangian submanifold to any embedded submanifold of Euclidean space. The invariant of the embedding will be the contact homology of this Lagrangian. Though the definition of this invariant is somewhat complicated it is possible to compute it for knots in Euclidean 3-space. Lenny Ng has combinatorially studied this invariant for such knots and has shown that it does not seem to be determined by previously known invariants but non the less has some connections with the classical Alexander polynomial of a knot. I will concentrate on the more geometric aspects of the invariant and ongoing work of Tobias Ekholm, Lenny Ng, Michael Sullivan and myself aimed at a better understanding of the invariant (in particular, showing that it is well defined in some generality).
There will be coffee and cookies in the lounge at 3:00.

Thursday, October 25, 2007

Posted September 14, 2007

3:40 pm - 4:30 pm Lockett 285 Originally scheduled for 3:30 pm, Thursday, October 11, 2007

Alex Iosevich , University of Missouri-Columbia
Some examples of interaction between harmonic analysis, geometric measure theory, combinatorics and number theory

Abstract: Many problems stated in analytic terms often turn out to be, in
essence, problem in combinatorics or number theory. The opposite phenomenon,
where number theoretic or combinatorical problems are fundamentally analytic in
nature is equally ubiquitous. We shall discuss this phenomonon from a
systematic point of view and will outline mechanisms that allow one to transfer
techniques and ideas from area to another.

There will be coffee and cookies in the lounge at 3:00.

Thursday, November 8, 2007

Posted September 14, 2007

3:40 pm - 4:30 pm Lockett 285

Clint Dawson, University of Texas at Austin
Simulation of Coupled Ground Water/Surface Water Flow

Abstract: There is strong evidence that the supply and quality of water are influenced by interactions between water stored at the surface and water stored in the subsurface. There have been a few efforts at modeling this interaction, but a number of outstanding questions still remain. In this talk we will address the mathematical modeling and numerical simulation of coupled ground water/surface water flow. Mathematical modeling issues include determining the appropriate models of flow within each subdomain, and determining the interface or boundary conditions to couple the models. Given a model, the next question is how to solve it. Here we will discuss an approach based on the discontinuous Galerkin (DG) method. A priori error analysis for a DG formulation for a shallow water model coupled with saturated ground water flow will be presented. Numerical results will also be discussed for several practical scenarios. We will also discuss recent analysis and results for a simplified surface water flow model, the diffusive wave approximation.

There will be coffee and cookies in the lounge at 3:00.

Thursday, November 29, 2007

Posted November 12, 2007

3:40 pm - 4:30 pm Lockett 285

Michael Lacey, Georgia Institute of Technology
Pointwise convergence of Fourier series

Abstract: Lennart Carleson's celebrated theorem on the pointwise convergence of Fourier series was one of three results cited by the Abel Prize committee, in making their award to him. This result states that any square integrable function on the unit circle is the limit, almost everywhere, of the Fourier partial sums. We will recall the theorem, explain why it is worthy of an Abel prize, and give a brief description of a proof. The theorem is related, even required, for a range of related questions, a much more recent development investigated by the speaker and Christoph Thiele, among many others. We close with a very recent new result of Victor Lie on the Quadratic Carleson Theorem.

There will be coffee and cookies in the lounge at 3:00.

Friday, February 1, 2008

Posted January 23, 2008

3:40 pm - 4:30 pm Lockett 277

Jan Dijkstra, Vrije Universiteit Amsterdam
Homeomorphism groups of manifolds and Erdös space

There is an abstract available.

There will be coffee and cookies in the lounge at 3:00.

Thursday, February 28, 2008

Posted January 22, 2008

3:40 pm - 4:30 pm Lockett 285

Dan Barbasch, Cornell University
Unipotent representations and unitarity

An abstract is available.
There will be coffee and cookies in the lounge at 3:00.

Thursday, March 6, 2008

Posted January 29, 2008

3:40 pm - 4:30 pm Lockett 285

Joseph Wolf, University of California, Berkeley
Limits of nilpotent commutative spaces

An abstract is available.

There will be coffee and cookies in the lounge at 3:00.

Thursday, March 27, 2008

Posted March 17, 2008

3:40 pm - 4:30 pm Lockett 285

Toshiyuki Kobayashi, Harvard and University of Tokyo
Existence Problem of Compact Locally Symmetric Spaces.

Abstract: The local to global study of geometries was a major trend of 20th
century geometry, with remarkable developments achieved particularly in
Riemannian geometry. In contrast, in areas such as Lorentz geometry,
familiar to us as the space-time of relativity theory, and more generally
in pseudo-Riemannian geometry, as well as in various other kinds of
geometry (symplectic, complex geometry, ...), surprising little is known
about global properties of the geometry even if we impose a locally
homogeneous structure.

I will give a survey on the recent developments regarding the question
about how the local geometric structure affects the global nature of
non-Riemannian manifolds, with emphasis on the existence problem of compact
forms, rigidity and deformation.

There will be coffee and cookies in the lounge at 3:00.

Thursday, April 3, 2008

Posted February 17, 2008

3:40 pm - 4:30 pm Lockett 285

Ron Goldman, Department of Computer Science, Rice University
Three Problems in Search of a Graduate Student

Abstract: Three unsolved problems that originated from research in
Computer Graphics and Geometric Modeling will be presented. The first
problem involves understanding the notion oscillation for Bezier
surfaces, the freeform surfaces most common in Computer Graphics and
Geometric Modeling. The second problem is related to Bezier curves and
univariate Bernstein polynomials, and concerns the combinatorics of
symmetrizing multiaffine functions. The third problem pertains to
fractals and asks if there is an algorithm to determine whether two
arbitrary sets of contractive affine transformations generate the same
fractal.

There will be coffee and cookies in the lounge at 3:00.

Thursday, April 10, 2008

Posted January 22, 2008

3:40 pm - 4:30 pm Lockett 285

Oleg Viro, SUNY Stony Brook
Compliments to bad spaces

Abstract: Could Mathematics be made any better by a different choice of basic definitions? Definitions in some mathematical theories exclude any mentioning of objects, which are believed to be nasty. We will consider few examples of such "political correctness". Speaking on differential manifolds, we usually pretend that they have no singular siblings. This causes lots of inconveniences. Another example is finite topological spaces. Most of mathematicians believe that all finite topological spaces are either trivial or nasty. Topology appears to be the only mathematical field that feels ashamed of its finite objects.

There will be coffee and cookies in the lounge at 3:00.

Thursday, September 25, 2008

Posted September 16, 2008

3:40 pm - 4:30 pm Lockett 235

Ravi Rau, Department of Physics and Astronomy, LSU
Possible links between physics problems in quantum computing and fibre bundles, projective geometry and coding/design theory

Abstract:
Quantum Information, the field that embraces quantum computing,
cryptography and teleportation, involves as a central object an
entangled pair of spin-1/2 (or two-level) systems. I have been
interested in developing geometrical pictures for manipulating the
fifteen-operator su(4) algebra that describes such systems. For a
single spin, its su(2) algebra's fibre bundle of a two-sphere
(called Bloch sphere by physicists) and a u(1) phase plays a major
role throughout the field of magnetic resonance. I will present
analogous geometrical descriptions of fibre bundles for su(4) and
its sub-algebras (and also higher su(N)). One of these sub-algebras,
su(2) X su(2) X u(1), also "maps" onto octonions and the Fano Plane.
Other sub-algebras and the full su(4) can be similarly related to
Desargues's and other diagrams of projective geometry. These relate
to the subjects of coding and design theory, and Hadamard matrices.
I am looking for help from mathematical experts in each of these
areas to see how these connections may be exploited for application
in quantum information.

There will be coffee and cookies in the lounge at 3:00.

Thursday, October 23, 2008

Posted September 19, 2008

3:40 pm - 4:30 pm Lockett 235

Ricardo Cortez, Tulane University
Regularized Stokeslets and other elements with applications to biological flows

Biological flows, such as those surrounding swimming microorganisms or beating cilia, are often modeled using the Stokes equations due to the small length scales. The organism surfaces can be viewed as flexible interfaces imparting force on the fluid. I will present the Method of Regularized Stokeslets and other elements that are used to compute Stokes flows interacting with immersed flexible bodies or moving through obstacles. The method treats the flexible bodies as sources of force or torque in the equations and the resulting velocity is the superposition of flows due to all the elements. Exact flows are derived for forces that are smooth but supported in small spheres, rather than point forces. I will present the idea of the method, some of the known results and several examples from biological applications.

There will be coffee and cookies in the lounge at 3:00.

Thursday, October 30, 2008

Posted August 28, 2008

3:40 pm - 4:30 pm Lockett 235

Mihai Putinar, University of California at Santa Barbara
Poincare's variational problem in potential theory

Abstract: The simultaneous diagonalization of two quadratic forms

naturally attached to a domain in the Euclidean space has

guided Poincare in his sudy of the Dirichlet problem. Put in modern

setting, due to a pioneering work of Mark G. Krein, Poiancare's

variational principle offers a deep understanding of modern aspects of

function theory (quasiconformal mappings, Beurling-Schiffer transform)

and provides the theoretical background of some recent studies

of an inverse problem in electrostatics. Based on joint work

with D. Khavinson and Harold S. Shapiro.

There will be coffee and cookies in the lounge at 3:00.

Thursday, November 13, 2008

Posted October 27, 2008

3:40 pm - 4:30 pm Lockett 235

Jinhyun Park, Purdue University
What can an algebraist do for Euclidean geometry?

Abstract: The 3rd problem of Hilbert, one of the firstly solved
Hilbert problems, studied the scissors congruence for the
3-dimensional Euclidean space: two polyhedra are said to be in
scissors congruence if one can cut the first along straight lines and
reassemble the components to get the second. Are all polyhedra of a
fixed volume then scissors congruent? The answer was negatively given
by Max Dehn, a student of Hilbert in around 1900. Though the problem
was solved, it opened many new doors during the next 100 years. We
will describe this problem from scratch, and mention how it is related
to some number theoretic questions and how it mysteriously gives new
problems in algebraic geometry.

There will be coffee and cookies in the lounge at 3:00.

Tuesday, November 18, 2008

Posted November 11, 2008

3:40 pm - 4:30 pm Lockett 235

Ivo Babuska, Institute for Computational Engineering and Sciences, University of Texas, Austin
Computational Science, Mathematics and Where Are We Going

Abstract: A major goal of Computational Science is to predict physical
and other phenomena. The problem is how confident can we be that the
computed results describe reality well enough so that they can be the
basis for crucial decisions. ( Do we have enough courage to sign the
blueprints based on the computation?) The notions of Verification and
Validation and their mathematical contains will be explained. These
notions are the basis for the confidence that the computed results
could be used for the decisions. A few examples of engineering
accidents and their reasons will be presented. Brief comments of the
repercussions for the educations at the universities will be
made. References to the basic literature will be given.

There will be coffee and cookies in the lounge at 3:00.

Thursday, January 15, 2009

Posted December 8, 2008

3:40 pm - 4:30 pm Lockett 285 (provisionally)

Burak Aksoylu, Department of Mathematics and CCT
Rigorously Justified Solvers for Rough Coefficients

Abstract:
Roughness of PDE coefficients causes loss of robustness of
preconditioners. The main goal is to recover robustness and obtain
rigorous structural understanding of the involved process. A
qualitative understanding of the PDE operators and their dependence on
the coefficients is essential for designing preconditioners. This
process draws heavily upon effective utilization of theoretical tools.

According to experience, the performance of a preconditioner depends
essentially on the degree to which the preconditioned operator
approximates the properties of the underlying infinite dimensional
operator. For this reason, controlling the infinite dimensional
problem provides a basis for the construction of preconditioners. We
use tools from operator theory for this. On the other hand, another
basis is the control of the finite dimensional discretized
problem. For that, we use singular perturbation analysis (SPA). After
obtaining a preconditioner through SPA, a fundamental need is to
explain the effectiveness of the preconditioner and to justify that
rigorously. With the insights provided by operator theory and SPA, we
are in control of the effectiveness and computational feasibility
simultaneously.

Based on ideas developed for porous media flow, we present a new
preconditioning strategy which is computationally comparable to
algebraic multigrid, but with rigorous justification. We will also
demonstrate how SPA gives valuable insight to the asymptotic behavior
of the solution of the underlying PDE, hence, provides feedback for
preconditioner construction.

There will be coffee and cookies in the lounge at 3:00.

Tuesday, January 27, 2009

Posted December 8, 2008

3:40 pm - 4:30 pm Lockett 285 (provisionally)

Michael Shapiro, Escuela Superior de Fisica y Matematicas del Instituto Politecnico Nacional, Mexico
On some basic ideas of hypercomplex analysis

Abstract: "Hypercomplex analysis" is a generic name for those
generalizations of one-dimensional complex analysis which involve
hypercomplex numbers. Quaternionic analysis is the oldest and the
most known version of it. In the talk, it will be discussed, first of
all, in which sense quaternionic analysis is a "proper" or a
"closest" version in low dimensions which includes as particular
cases, or sub-theories, such classic theories as vector analysis and
holomorphic mappings in two complex variables, as well as some
systems of partial differential equations. This allows one, by
developing quaternionic analysis, to obtain new results for the above
classic theories and to refine known ones; some applications of this
approach to harmonic analysis, operator theory, mathematical
physics, will be mentioned. Some comments on Clifford analysis and
its applications will be also made.

There will be coffee and cookies in the lounge at 3:00.

Thursday, January 29, 2009

Posted December 8, 2008

3:40 pm - 4:30 pm Lockett 285 (provisionally)

Maria Elena Luna-Elizarraras, Escuela Superior de Fisica y Matematicas del Instituto Politecnico Nacional, Mexico
On functional analysis with quaternionic scalars

Here is an abstract.

There will be coffee and cookies in the lounge at 3:00.

Thursday, March 5, 2009

Posted February 2, 2009

3:40 pm - 4:30 pm Lockett 285

Stephen Sawin, Fairfield University
Supersymmetry, Quantum Mechanics and the Gauss-Bonnet-Chern Theorem

Abstract: In joint work with Dana Fine at UMass Dartmouth, we will give a
rigorous construction of the path integral describing the time-
evolution operator for imaginary time quantum mechanics, with and
without $N=1$ supersymmetry. The path integral is constructed as a
limit of finite-dimensional approximating integrals, with concrete
uniform estimates on the convergence. Consequences of this include
an alternative construction of the Laplace and Laplace-Beltrami heat
kernels. We will use this construction to give a rigorous version of
Witten/Alvarez-Gaumé/Friedan and Windey's path integral "proof"
of the Gauss-Bonnet-Chern Theorem, and explain how we expect a minor
variation to make rigorous their proof of the general Index Theorem.

There will be coffee and cookies in the lounge at 3:00.

Thursday, March 12, 2009

Posted February 19, 2009

3:40 pm - 4:30 pm Lockett 285

Charles Livingston, Indiana University
Four-dimensional aspects of classical knot theory

Abstract: Classical knot theory studies knots in 3-space; that is, embeddings of the unit circle, S^1, into R^3. Higher dimensional knot theory generalizes this, for instance by considering embeddings of the 2-sphere, S^2, into R^4. In this talk I will discuss an aspect of knot theory between the low and high-dimensional realms: the study of knots in 3-space in terms of the surfaces they bound in upper 4-space, H^4, the set of points (x,y,z,w) in R^4 with w > 0. Three of the goals of the presentation will be to: (1) give some intuitive insight into how knots can bound such surfaces; (2) describe a few of the central topics in geometric topology that motivate looking at knots in this way; and (3) summarize some recent advances in the area.

There will be coffee and cookies in the lounge at 3:00.

Tuesday, March 17, 2009

Posted February 10, 2009

3:40 pm - 4:30 pm Lockett 285

Stratos Prassidis, Canisius College
Detecting Linear Groups

Abstract: Linear groups are subgroups of general linear groups. Deciding if
a group is linear or not is an old problem in group theory. Linear groups
became important in topology after the Isomorphism Conjecture was proved for
discrete linear groups. We present criteria that guarantee that a group is
linear and some applications. At the end, we will show a hands-on proof that
the holomorph of the free group on two generators is linear.

There will be coffee and cookies in the lounge at 3:00.

Thursday, March 19, 2009

Posted February 2, 2009

3:40 pm - 4:30 pm Lockett 285

Jiazu Zhou, Southwest University, China
Geometric measures and geometric inequalities

An abstract is available.

There will be coffee and cookies in the lounge at 3:00.

Thursday, April 2, 2009

Posted March 26, 2009

3:40 pm - 4:30 pm Lockett 285

Gregor Masbaum, University Paris 7
Trees , Pfaffians and Complexity (or How not to win a million dollars)

There will be coffee and cookies in the lounge at 3:00.

Thursday, April 23, 2009

Posted April 12, 2009

2:40 pm - 3:30 pm Lockett 285 Originally scheduled for 3:30 pmMonday, April 20, 2009

Ivan Dimitrov, Queen's University (Canada)
A geometric realization of extreme components of the tensor product of modules over algebraic groups

Abstract: In this talk I will explain how the celebrated theorem of
Borel-Weil-Bott provides a natural realization of some extreme
components of the tensor product of two irreducible modules of simple
algebraic groups. I will also discuss a number of connections of our
construction with problems coming from Representation Theory,
Combinatorics, and Geometry, including questions about the
Littlewood--Richardson cone related to Horn's conjecture, settled by
Knutson and Tao in the late 1990's.

The talk is based on a joint work with Mike Roth.

There will be coffee and cookies in the lounge at 2:00.

Thursday, August 27, 2009

Posted August 11, 2009

3:40 pm - 4:30 pm Lockett 285

Pramod Achar, Mathematics Department, LSU
Positivity, sheaves, and representation theory

Abstract:
The celebrated "Kazhdan-Lusztig polynomials" of an algebraic group have an
elementary combinatorial definition, but the proof that all their
coefficients are nonnegative requires very deep results from algebraic
geometry--the Weil conjectures, proved by Deligne in the 1970's. The link
between combinatorics and algebraic geometry is furnished by sheaf theory,
especially the so-called "perverse sheaves." I will explain how
"positivity" results come out of the interaction of these topics, and I will
also discuss more recent developments in which perverse sheaves are replaced
by vector bundles and coherent sheaves.

There will be coffee and cookies in the lounge at 3:00.

Friday, September 4, 2009

Posted August 11, 2009

3:40 pm - 4:30 pm Lockett 285

Habib Ouerdiane, University of Tunis El Manar
Generalized fractional evolution equations

Abstract:
In this talk we study the generalized Riemann-Liouville (resp. Caputo)
time fractional evolution equation in infinite dimensions. We show that
the explicit solution is given as the convolution between the initial
condition and a generalized function related to the Mittag-Leffler
function. The fundamental solution corresponding to the Riemann-Liouville
time fractional evolution equation does not admit a probabilistic
representation while for the Caputo time fractional evolution equation
it is related to the inverse stable subordinators.

There will be coffee and cookies in the lounge at 3:00.

Thursday, September 10, 2009

Posted August 11, 2009

3:40 pm - 4:30 pm Lockett 285

Fernanda Cipriano, University of Lisbon
Statistical solutions for the 2D Euler equation

Abstract:
In the study of Euler and Navier-Stokes equations we can consider two
different approaches. The most classical one consist in the study of the
equations with specifique initial and boundary conditions.
Another approach, the so-called stochastic approach, consist in the
construction of suitable probability measures and study its evolution
in time according to the corresponding dynamic. The framework of
stochastic analysis can be used to construct solutions. In our
presentation, we follow the second point of view to present some
results on the 2D Euler equation with periodic boundary conditions.
We construct surface type measures on the level sets of the renormalized
energy and establish the existence of weak solutions living on such level
sets. We also prove the existence of weak solutions for the forward and
backward transport equations associated with the 2D Euler equation. Such
solutions can be interpreted, respectively, as a statistical Lagrangean
and statistical Eulerian description of the motion of the fluid.

There will be coffee and cookies in the lounge at 3:00.

Thursday, September 17, 2009

Posted August 11, 2009

3:40 pm - 4:30 pm Lockett 285

Milen Yakimov, LSU
Poisson geometry of flag varieties, ring theory and combinatorics

Abstract:
The geometry of Poisson Lie groups and Poisson homogeneous spaces was
actively studied after Drinfeld's celebrated 1986 ICM talk in which he
describe its importance for the representation theory of quantum groups.

In this talk we will go over various aspects of the geometry of Poisson
structures on flag varieties for complex simple Lie groups
(results with K. Brown and K. Goodearl). We will apply them to ring theory
to resolve several problems for the De Concini-Kac-Procesi algebras from
about 10-15 years ago: determining the torus invariant prime ideals of those
algebras, their inclusions, finding effective generating sets for the
ideals. We will also describe applications to combinatorics: 1. obtaining a
simple proof of the recent result of Knutson, Lam and Speyer for cyclicity
of the Lusztig stratification of Grassmannians, 2. combinatorial formulas
for Hecke algebras (with F. Brenti), 3. Deodhar's stratification of open
Richardson varieties (with B. Webster).

There will be coffee and cookies in the lounge at 3:00.

Monday, September 21, 2009

Posted July 27, 2009

3:40 pm - 4:30 pm Lockett 285

Stephen Smith, University of Illinois Chicago Circle
Revisiting the classification of the finite simple groups (an outline)

Abstract:
Most mathematicians are aware that the classification of
the finite simple groups involved hundreds of researchers
and thousands of journal pages.
In 1983, Daniel Gorenstein published the first volume
of a general outline of this massive work---covering the
non-characteristic 2 type'' case (correspondingly
roughly to simple matrix groups over fields of odd order).

But he could not publish the projected second and final volume,
on the characteristic 2 type case---due to the non-publication
of Mason's expected work on "quasithin groups". That gap was not
filled until the 2004 publication by Aschbacher and Smith
of a more general quasithin treatment.
This finally left the way open for the second volume of the overall
outline of the CFSG---a first draft of this outline has now been completed
by Aschbacher, Lyons, Solomon, and Smith.

The talk will be an elementary exposition of some of the
ideas in this overall outline; including mention of certain
of the new ideas and approaches which have arisen since the 1980s.

There will be coffee and cookies in the lounge at 3:00.

Thursday, October 8, 2009

Posted August 11, 2009

3:40 pm - 4:30 pm Lockett 285

Dmitry Ryabogin, Kent State University
On the local version of Mahler Conjecture

An abstract is available.

There will be coffee and cookies in the lounge at 3:00.

Tuesday, November 3, 2009

Posted August 11, 2009

3:40 pm - 4:30 pm Lockett 285

Irina Mitrea, Worcester Polytechnic Institute
Boundary Value Problems for Higher Order Elliptic Operators

An abstract is available.

There will be coffee and cookies in the lounge at 3:00.

Tuesday, January 19, 2010

Posted January 12, 2010

2:00 pm - 3:00 pm Lockett 16

Jiajun Wang, California Institue of Technology Candidate for Assistant Professor Position in Topology
On combinatorial Floer homology

Posted January 7, 2010

3:40 pm - 4:30 pm 338 Johnston Hall

Jason Howell, Carnegie Mellon University Candidate for Assistant Professor Position in Math and CCT
Dual-Mixed Finite Element Methods For Fluids

Jason Howell, Carnegie Mellon University Postdoctoral Associate In The Center For Nonlinear Analysis And The Department Of Mathematical Sciences Bio Jason Howell is a Postdoctoral Associate in the Center for Nonlinear Analysis and the Department of Mathematical Sciences at Carnegie Mellon University. He earned a PhD in Mathematical Sciences at Clemson University in 2007 with a specialty in numerical analysis and computational mathematics. During 2004-2006, he had three appointments as a summer scholar with the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. He also holds an MS in Mathematical Sciences from Clemson and a BS in Mathematics from the College of Charleston. His research interests lie at the intersection of analysis, computation, and applications, and he currently works on projects in finite element methods for fluid and solid mechanics, numerical methods for non-Newtonian fluids, and numerical methods for fluid/fluid and fluid/structure interaction problems. Abstract Accurate and efficient numerical methods to approximate fluid flows are important to researchers in many fields, including mechanical, materials, and biomedical engineering. In many applications within these fields, it is of paramount importance to accurately predict fluid stresses. However, in most existing numerical schemes for fluids, the primary unknown of interest is the fluid velocity. This motivates the development of dual-mixed finite element methods for fluids, in which the stress is a primary unknown of interest, and the study of inf-sup conditions for single and twofold saddle point problems is an important component of the construction of these methods. This study has led to results that give equivalent sets of inf-sup conditions for twofold saddle point problems, yielding new tools for proofs of well-posedness and finite element compatibility. These tools, together with a macroelement technique, show compatibility of a new dual-mixed method for fluids employing Arnold-Winther symmetric tensor finite elements for stress.

Thursday, January 21, 2010

Posted January 7, 2010

2:00 pm - 3:00 pm 338 Johnston Hall

Shawn Walker, New York University Candidate for Assistant Professor Position in Math and CCT
Shape Optimization Of Peristaltic Pumping

Shawn W. Walker, New York University

Research Scientist, Courant Institute Of Mathematical Sciences

Bio

Shawn W. Walker is a postdoctoral researcher and instructor at New York University's Courant Institute of Mathematical Sciences. He earned his PhD in aerospace engineering and an MSc in applied mathematics and scientific computing from the University of Maryland in 2007 and also holds an MSc in engineering and applied science from Yale University and a BSc in electrical engineering from Virginia Polytechnic Institute & State University. His research interests include finite element methods and PDEs, free boundary problems, shape optimization, and fluid-structure interaction and control. http://www.cims.nyu.edu/~walker/

Abstract

Transport is a fundamental aspect of biology and peristaltic pumping is a fundamental mechanism to accomplish this; it is also important in many industrial processes. We present a variational method for optimizing peristaltic pumping in a two dimensional periodic channel with moving walls to pump fluid. No a priori assumption is made on the wall motion, except that the shape is static in a moving wave frame. Thus, we pose an infinite dimensional optimization problem and solve it with finite elements. Sensitivities of the cost and constraints are computed variationally via shape differential calculus and $L^2$-type projections are used to compute quantities such as curvature and boundary stresses. Our Optimization method falls under the category of sequential quadratic programming (SQP) methods. As a result, we find optimized shapes that are not obvious and have not been previously reported in the peristaltic pumping literature. Specifically, we see highly asymmetric wave shapes that are far from being sine waves. Many examples are shown for a range of fluxes and Reynolds numbers up to Re=500 which illustrate the capabilities of our method.

Posted December 24, 2009

3:40 pm - 4:30 pm Lockett 285

Jan Dijkstra, Vrije Universiteit Amsterdam
Topological Kadec norms with applications

An abstract is available.

There will be coffee and cookies in the lounge at 3:00.

Friday, January 22, 2010

Posted January 12, 2010

3:40 pm - 4:30 pm Lockett 285

Andrew Putman, MIT Candidate for Assistant Professor Position in Topology
The Picard Group of the Moduli Space of Curves with Level Structures

Tuesday, January 26, 2010

Posted January 14, 2010

2:10 pm Lockett 10

Richard Kent, Brown University Candidate for Assistant Professor Position in Topology
Analytic functions from hyperbolic manifolds

There will be coffee and cookies in the lounge at 3:00.

Posted January 7, 2010

3:40 pm - 4:30 pm Lockett 285

Michael Farber, University of Durham
Stochastic algebraic topology and robotics

Abstract: I will describe solutions to several problems of mixed
probabilistic-topological nature which are inspired by applications in
topological robotics. These problems deal with systems depending on a
large number of random parameters, nto infty. Our results predict
the values of various topological characteristics of configuration
spaces of such systems.

There will be coffee and cookies in the lounge at 3:00.

Wednesday, January 27, 2010

Posted January 12, 2010

3:40 pm - 4:30 pm Lockett 285

Mark Colarusso, University of Notre Dame Candidate for Assistant Professor Position in Lie Theory
THE GELFAND-ZEITLIN INTEGRABLE SYSTEM ON g[(n, C)

Thursday, January 28, 2010

Posted August 11, 2009

3:40 pm - 4:30 pm Lockett 285 Originally scheduled for 3:30 pmTuesday, September 15, 2009

Frank Sottile, Texas A&M
Orbitopes

Abstract:
An orbitope is the convex hull of an orbit of a compact
group acting linearly on a vector space. Instances of these
highly symmetric convex bodies have appeared in many areas
of mathematics and its applications, including protein
reconstruction, symplectic geometry, and calibrations in
differential geometry.
In this talk, I will discuss Orbitopes from the perspectives
of classical convexity, algebraic geometry, and optimization
with an emphasis on ten motivating problems and concrete examples.
This is joint work with Raman Sanyal and Bernd Sturmfels.

There will be coffee and cookies in the lounge at 3:00.

Friday, January 29, 2010

Posted January 14, 2010

3:40 pm - 4:30 pm Lockett 285

Richard Oberlin, UCLA Candidate for Assistant Professor Position in Analysis
A variation-norm Carleson Theorem

Monday, February 1, 2010

Posted January 13, 2010

3:40 pm - 4:30 pm Lockett 285

Karl Schwede, University of Michigan Candidate for Assistant Professor Position in algebraic geometry
Singularities of polynomials in characteristic 0 and characteristic p

Tuesday, February 2, 2010

Posted January 7, 2010

3:40 pm - 4:30 pm 338 Johnston Hall

Xuemin Tu Candidate for Assistant Professor Position in Math and CCT
Inexact Balancing Domain Decomposition By Constraints Algorithms

Abstract and Bio available at www.cct.lsu.edu

Monday, February 8, 2010

Posted January 15, 2010

3:40 pm - 4:30 pm Lockett 285

Juhi Jang, New York University Candidate for Assistant Professor Position in PDEs/applied math
Vacuum in Gas and Fluid dynamics

Tuesday, February 9, 2010

Posted January 7, 2010

3:40 pm - 4:30 pm 338 Johnston Hall

Yingda Cheng Candidate for Assistant Professor Position with Math and CCT
Discontinuous Galerkin Finite Element Methods And Applications To Boltzmann-Poisson Models In Semiconductor Device Simulation

Abstract and Bio at www.cct.lsu.edu

Thursday, February 11, 2010

Posted January 15, 2010

2:00 pm - 3:00 pm Lockett 112

Leonardo Mihalcea, Baylor University Candidate for Assistant Professor Position in Algebraic Geometry
Quantum K-Theory of Grassmannians and the Geometry of Spaces of Curves

Friday, February 12, 2010

Posted February 1, 2010

3:40 pm - 4:30 pm Lockett 285

John Oprea, Cleveland State University
Gottlieb Groups, LS Category and Geometry

Abstract: Gottlieb groups are special subgroups of the homotopy groups which
arise in many homotopical contexts. LS category is a numerical homotopy
invariant that was originally invented to give a bound on the number of
critical points of smooth functions. Strangely enough, these two things are
related, and --- what's more --- they are related via analogues of geometric
theorems. This talk will recall basic notions of algebraic topology,
introduce Gottlieb groups, LS category and their relationships and see how
geometry fits into the mix.

There will be coffee and cookies in the lounge at 3:00.

Thursday, February 18, 2010

Posted January 7, 2010

3:40 pm - 4:30 pm Lockett 285

Bojko Bakalov, North Carolina State University
Singularities, root systems, and W algebras

Abstract:
Gromov-Witten invariants are naturally organized in a generating function,
which is a formal power series in infinitely many variables. In many cases
this function is a highest-weight vector for a certain
infinite-dimensional algebra and at the same time is a solution of an
integrable hierarchy of partial differential equations. Similar generating
functions can be introduced for the Frobenius structures coming from
singularities of hypersurfaces. We will start by reviewing the marvelous
relations among singularities, root systems and reflection groups. The
generating function of a simple singularity was shown recently to be a
solution of the Kac-Wakimoto hierarchy. Our main result is that it is also
a highest weight vector for the corresponding W algebra.

There will be coffee and cookies in the lounge at 3:00.

Thursday, February 25, 2010

Posted February 9, 2010

3:40 pm - 4:30 pm Lockett 285

Scott Armstrong, Department of Mathematics, Louisiana State University
The infinity Laplace equation, tug-of-war games, and minimizing Lipschitz extensions

Abstract: Given a nice bounded domain, and a Lipschitz function defined on
its boundary, consider the problem of finding an extension of this
function to the closure of the domain which has minimal Lipschitz
constant. This is the archetypal problem of the calculus of variations
in $L^\infty$. There can be many such minimal Lipschitz extensions,
but there is there is a unique minimizer once we properly "localize"
this Lipschitz minimizing property. The uniquely specified function is
a solution of the infinity Laplace equation: the Euler-Lagrange
equation for our optimization problem. This PDE is a highly degenerate
nonlinear elliptic equation which does not have smooth solutions. In
this talk we will discuss what we know about the infinity Laplace
equation, what the important open questions are, and some recent
developments. We will even play a two-player random-turn game called
"tug-of-war". One advantage of our topic is that it is completely
accessible to graduate students and even perhaps some undergraduates.

There will be coffee and cookies in the lounge at 3:00.

Wednesday, March 10, 2010

Posted March 3, 2010

2:40 pm - 3:30 pm Prescott 205

Gisele Goldstein, University of Memphis
Derivation and Interpretation of Dynamic Boundary Conditions for the Heat and Wave Equations

There is an abstract available.

There will be coffee and cookies in Prescott 205 at 2:00.

Thursday, March 11, 2010

Posted March 3, 2010

2:10 pm - 3:00 pm Lockett 10

Jerome Goldstein, University of Memphis
Instantaneous blowup and related nonexistence issues

An abstract is available.

There will be coffee and cookies in the lounge at 3:00.

Thursday, March 25, 2010

Posted January 27, 2010

3:40 pm - 4:30 pm Lockett 285

Charles Weibel, Rutgers University
The Lichtenbaum and Bloch-Kato Conjectures are now Theorems

Abstract: The Lichtenbaum Conjecture related algebraic K-theory of the
integers to the values of the Riemann Zeta function. The Bloch-Kato
Conjecture said that the etale cohomology of a field with (odd) finite
coefficients) should have a presentation with units as generators and
simple quadratic relations (the ring with this presentation is now
called the "Milnor K-theory"). For Z/2 coefficients, this is a
famous theorem of Voevodsky.

This talk will be a non-technical overview of the ingredients that go
in to the proof, and why this conjecture matters to non-specialists.
Most of the ingredients are due to Rost and Voevodsky.

Here is a fun consequence of all this. We now know the first 20,000
groups K_n(Z) of the integers, except when 4 divides n. The assertion that
these groups are zero when 4 divides n (n>0) is equivalent to Vandiver's
Conjecture (in number theory), and if it holds then we have fixed Kummer's
1849 "proof" of Fermat's Last Theorem. If any of them are nonzero, then the
smallest prime dividing the order of this group is at least 16,000,000.

There will be coffee and cookies in the lounge at 3:00.

Thursday, April 1, 2010

Posted January 7, 2010

3:40 pm - 4:30 pm Lockett 285

Boris Rozovsky, Brown University
Quantization of Stochastic Navier-Stokes Equation

Abstract: We consider a stochastic Navier-Stokes equation driven by a
space-time Wiener process. This equation is quantized by transformation of
the nonlinear term to the Wick product form. An interesting feature of this
type of perturbation is that it preserves the mean dynamics: the expectation
of the solution of the quantized Navier-Stokes equation solves the
underlying deterministic Navier-Stokes equation. From
the stand point of a statistician it means that the perturbed model is an
unbiased random perturbation of the deterministic Navier-Stokes equation.

The quantized equation is solved in the space of generalized stochastic
processes using the Cameron-Martin version of the Wiener chaos expansion. A
solution of the quantized version is unique if and only if the uniqueness
property holds for the underlying
deterministic Navier-Stokes equation. The generalized solution is obtained
as an inverse of solutions to corresponding quantized equations. We will
also demonstrate that it could be approximated by real (non-generalized
processes). A solution of the
quantized Navier-Stokes equation turns out to be non- anticipating and
Markov.

The talk is based on a joint work with R. Mikulevicius.

There will be coffee and cookies in the lounge at 3:00.

Thursday, April 22, 2010

Posted March 2, 2010

3:40 pm - 4:30 pm Lockett 285

Ben Webster, MIT
Categorification, Lie algebras and topology

Abstract:
It's a long established principle that it is interesting to think
about numbers as the sizes of sets, or as the dimensions of vector spaces,
or better yet, as the Euler characteristic of complexes. You can't have a
map between numbers, but you can have one between sets or vector
spaces. For example, the Euler characteristic of topological spaces is not
functorial, but homology is.

One can try to extend this idea to a bigger stage, by, say, taking a
vector space and trying to make a category by defining morphisms
between its vectors. This approach, interpreted suitably, has been a
remarkable success with the representation theory of semi-simple Lie
algebras (and their associated quantum groups). I'll give an
introduction to this area, with a view toward applications in
topology; in particular to replacing polynomial invariants of knots
that come from representation theory with vector-space-valued
invariants that reduce to knot polynomials under Euler characteristic.

There will be coffee and cookies in the lounge at 3:00.

Thursday, April 29, 2010

Posted January 7, 2010

3:40 pm - 4:30 pm Lockett 285

Alexander Its, Indiana University-Purdue University Indianapolis
Special Functions and Integrable Systems

Abstract:
The recent developments in the theory of integrable systems
have revealed its intrinsic relation to the theory of special functions.
Perhaps the most generally known aspects of this relation are
the group-theoretical, especially the quantum-group theoretical,
and the algebra-geometrical ones. In the talk we will discuss
the analytic side of the Special Functions-Integrable Systems
connection. This aspect of the relation between the two theories
is less known to the general mathematical community,
although it goes back to the classical works of Fuchs, Garnier and
Schlesinger on the isomonodrony deformations of the systems of linear
differential equations with rational coefficients. Indeed, the monodromy
theory of linear systems provides a unified framework for the linear
(hypergeometric type) and nonlinear (Painlev'e type) special functions
and, simultaneously, builds a base for the new powerful technique of the
asymptotic analysis - the Riemann-Hilbert method.

In this survey talk, which is based on the works of many authors
spanned over more than two decades, the isomonodromy point of view
on special function will be outlined. We will also review the history of
the Riemann-Hilbert method as well as its most recent applications in the
theory of orthogonal polynomials and random matrices.

Coffee and cookies: The James E. Keisler lounge, 3:00.

Thursday, September 23, 2010

Posted September 10, 2010

3:40 pm - 4:30 pm Lockett 277

Hongyu He, Department of Mathematics, LSU
Theta Correspondence and Unitary Representations

In the late 1950's and early 1960's, motivated by problems from physics
and number theory, Segal, Shale and Weil independently discovered a
projective representation of the symplectic group, often called the
oscillator representation. This representation was later used by
Kashiwara-Vergne and many others to obtain new unitary representation and
automorphic forms for other classical groups. The theory underlying these
developments is often called theta correspondence. In this talk, I will
review Howe's theory of reductive dual pair and theta correspondence. I
will then discuss how theta correspondence can be used to understand the
unitary dual of the noncompact orthogonal groups. With the exception of
rank-one groups and several higher rank groups, the unitary dual of the
noncompact orthogonal groups is not completely classified.

Thursday, September 30, 2010

Posted September 8, 2010

3:40 pm - 4:30 pm Lockett 277

Kalyan B. Sinha, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Index Theorems in Quantum Mechanics

Abstract: The notion of the Fredholm index of an operator is extended to
pairs of projections as well as to certain pairs of (unbounded)
self-adjoint operators in a Hilbert space. This index often exhibits
some invariance properties and has applications in Quantum mechanical
problems. There is also a K-theoretic description of the problem.

Thursday, October 28, 2010

Posted October 7, 2010

3:40 pm - 4:30 pm Lockett 277

Vladimir Dragovic, MI SANU, Belgrade/GFM University of Lisbon
Discriminant separability, Poncelet porisms and Kowalevski top

Abstract. A new view on the Kowalevski top and Kowalevski integration procedure is presented. It is based on a classical notion of Darboux coordinates, a modern concept of n-valued Buchstaber-Novikov groups and a new notion of discriminant separability. Unexpected relationship with the Great Poncelet Theorem for a triangle is established. Further connections between discriminant separability, geometry of pencils of quadrics and integrability are discussed.

Thursday, December 2, 2010

Posted September 29, 2010

3:40 pm - 4:30 pm Lockett 277

Dimitar Grantcharov, University of Texas at Arlington
Categories of weight representations of Lie algebras

Abstract: Following works of G. Benkart, D. Britten, S. Fernando, V. Futorny, A. Joseph, F. Lemire, and others, in 2000 O. Mathieu achieved a major breakthrough in representation theory by classifying the simple weight representations of Lie algebras. The next step in the study of weight representations is to look at the indecomposable representations. In this talk we will discuss recent results related to the structure of the indecomposable weight representations and connections with quiver theory and algebraic geometry. This is a joint work with Vera Serganova.

Thursday, January 20, 2011

Posted October 7, 2010

3:40 pm - 4:30 pm Lockett 277

Birgit Speh, Cornell University
Branching rules of unitary representations: Examples and applications to automorphic forms

One of the basic problems of representations theory is to understand how a representation is built up of irreducible representations. For finite dimensional representations of compact groups there exist well known combinatorial algorithms. In this talk we will examine the problem for infinite dimensional representations of semisimple Lie groups, give some examples as well as applications to automorphic forms and locally symmetric spaces.

Friday, January 21, 2011

Posted January 19, 2011

3:40 pm - 4:30 pm Lockett 277

Aaron Lauda, Columbia University
Categorifying quantum groups and link invariants

Abstract: The Jones polynomial can be understood in terms of the representation theory of the quantum group associated to the Lie algebra sl2. This description facilitated a vast generalization of the Jones polynomial to other quantum link and tangle invariants called Reshetikhin-Turaev invariants. These invariants, which arise from representations of quantum groups associated to simple Lie algebras, subsequently led to the definition of quantum 3-manifold invariants. In this talk we categorify quantum groups using a simple diagrammatic calculus that requires no previous knowledge of quantum groups. These diagrammatically categorified quantum groups not only lead to a representation theoretic explanation of Khovanov homology but also inspired Webster's recent work categorifying all Reshetikhin-Turaev invariants of tangles.

Monday, January 24, 2011

Posted January 21, 2011

9:40 am - 10:30 am Lockett 233

Elizabeth Dan-Cohen, Jacobs University Bremen
Structure and representation theory of finitary Lie algebras (virtual talk from Bremen)

ABSTRACT: Finitary Lie algebras are the simplest possible infinite-dimensional version of the classical Lie algebras. These infinite-dimensional algebras arise in many contexts in mathematics. However, their structure theory was underdeveloped until recently, and the representation theory is still in its early stages. I have been part of a recent series of contributions first to the structure and then most recently to the representation theory.

Tuesday, January 25, 2011

Posted November 26, 2010

3:40 pm - 4:30 pm Lockett 277

Vyacheslav Futorny, University of Sao Paulo
Representations of Lie algebra of vector fields on a torus

Representation theory of Lie algebra of vector fields on a circle, centerless Virasoro algebra, is well known due to results of O. Mathieu who proved Kac's conjecture. On the other hand, representations of Lie algebra of vector fields on n-dimensional torus are far less studied. We are going to discuss certain classes of representations whose construction is based on the theory of vertex algebras. These representations provide free-fields realizations of our Lie algebra. These are joint results with Yuly Billig (Ottawa, Canada).

Wednesday, January 26, 2011

Posted January 20, 2011

2:40 pm - 3:30 pm Lockett 285

John Baldwin, Princeton University
Contact structures, open books, and Khovanov homology

I will describe an important class of geometric objects on 3-manifolds called contact structures, and will survey Giroux's celebrated correspondence between contact structures and more topological objects called open books. I will summarize progress on some open questions related to this connection, and will explain how link invariants like Khovanov homology may be used to provide further insights.

Friday, January 28, 2011

Posted January 20, 2011

3:40 pm - 4:30 pm Lockett 277

Song Yao, University of Michigan
Optimal Stopping for Dynamic Convex Risk Measures

Abstract: We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who chooses the termination time of the game, and an agent (the "controller", or "nature") who selects the probability measure.

Wednesday, February 2, 2011

Posted January 20, 2011

3:40 pm - 4:30 pm Lockett 277

Karl Mahlburg, Princeton University
Percolation, partitions, and probability

I will discuss the surprising connections between finite-size scaling in families of bootstrap percolation models, the combinatorics of integer partitions, and limiting entropies for Markov-type processes. A combinatorial characterization of the percolation processes relates their metastability threshold exponents to the cuspidal asymptotics of generating functions for partitions with restricted sequence conditions. These generating functions are hypergeometric q-series that are of number-theoretic interest, as in many cases they are equal to the product of modular forms and Ramanujan's famous mock theta functions. In other cases, both the percolation processes and partition functions are best understood through entropy bounds for probabilistic sequences with gap conditions. These sequences can be understood as Markov-type processes with varying transition probabilities, and techniques from the theory of linear operators are used in order to bound the dominant eigenvalue.

Friday, February 4, 2011

Posted January 20, 2011

3:40 pm - 4:30 pm Lockett 277

Nam Quang Le, Columbia University
Regularity results for the mean curvature flow

Mean curvature flow is the evolution of a hypersurface moving with normal velocity equal to its mean curvature vector. If the initial hypersurface is compact then the flow will develop singularities in finite time. In this talk, we will present some recent regularity results on the compact mean curvature flow. Our focus will be on optimal conditions for the existence of smooth solutions to the mean curvature flow. We will show that if the flow is of type I then the mean curvature controls the flow in the sense that singularities cannot occur if the mean curvature is uniformly bounded. In the case of surfaces, we will show that the mean curvature controls the flow provided that either the Multiplicity One Conjecture of Ilmanen holds or the Gaussian density is less than two. When the mean curvature of our flow blows up, i.e., when singularities occur, we will also give its (sharp) blow-up rate.

Tuesday, February 8, 2011

Posted January 20, 2011

3:40 pm - 4:30 pm Lockett 277

Leonardo Mihalcea, Baylor University Candidate for Assistant Professor Position in Algebraic Geometry
Rational curves in flag manifolds and Gromov-Witten invariants

Abstract: Gromov-Witten (GW) invariants for a flag manifold count rational curves subject to certain incidence conditions. These numbers satisfy remarkable equations, equivalent to the associativity relations of the quantum cohomology algebra, and were successfully used to solve many classical problems in enumerative geometry. In connection to Mirror Symmetry and Integrable systems, Givental and his collaborators defined the equivariant and K-theoretic GW invariants, which allow the corresponding space of rational curves to be positive dimensional. The purpose of my talk is to introduce the "quantum=classical" phenomenon, which in many instances allows us to compute explicitly 3-point GW invariants (of all flavors), and to obtain algorithms for multiplication in the (generalized) quantum cohomology algebra. In the case of Grassmannians, this is surprisingly related to positroids - varieties connected to Lusztig's totally positive stratification.

Thursday, February 10, 2011

Posted November 8, 2010

3:40 pm - 4:30 pm Lockett 277

Robert Stanton, Ohio State University
Symplectic methods in Lie theory

Abstract: The non-degenerate Cartan-Killing form on a semisimple Lie algebra provides a natural conformal class of pseudo-Riemannian metric in Lie theory. The resulting interplay of differential geometry and harmonic analysis on Lie groups and symmetric spaces is well known. At the other extreme is the presence of a non-degenerate skew-symmetric form. We will illustrate the usefulness of symplectic techniques by several applications ranging from classical invariant theory to exceptional Lie algebras to modern differential geometry. The talk is intended for a general audience and is based on joint work with M. Slupinski.

Tuesday, February 15, 2011

Posted November 11, 2010

3:40 pm - 4:30 pm Lockett 277

Joseph Wolf, University of California, Berkeley
Classical Analysis and Nilpotent Lie Groups

Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I'll describe how this goes for nilpotent Lie groups and for a class of riemannian manifolds closely related to a nilpotent Lie group structure.

Thursday, February 24, 2011

Posted September 14, 2010

3:40 pm - 4:30 pm Lockett 277

Noriko Yui, Queen's University
The modularity (automorphy) of Calabi-Yau varieties over the rationals

Abstract: According to the Langlands Philosophy, every algebraic variety defined over the rationals or a number field should be modular (automorphic).

In this talk, I will concentrate on a special class of algebraic varieties, called Calabi-Yau varieties (of dimension at most three), defined over the rationals, and report on the current status of their modularity (automorphy).

Thursday, March 3, 2011

Posted October 29, 2010

3:40 pm - 4:30 pm Lockett 277

Skip Garibaldi, Emory University
Did a 1-dimensional magnet detect a 248-dimensional Lie group?

Abstract: In a January 2010 article in Science, a team of physicists reported that they had "detected evidence of E8 symmetry" in a neutron scattering experiment on a quasi-1-dimensional cobalt niobate magnet. Their article details their experimental results, but it does not explain how these are connected with E8, a 248-dimensional Lie group. This talk will survey the chain of reasoning leading from those results to E8.

This talk does not require any previous knowledge of advanced physics.

Tuesday, March 15, 2011

Posted January 8, 2011

3:40 pm - 4:30 pm Lockett 277

Grigory Litvinov, Independent University of Moscow
Dequantization and tropical mathematics

Tropical mathematics can be treated as a result of a dequantization of the traditional mathematics over numerical fields as the Planck constant tends to zero taking imaginary values. Tropical mathematics is a part of the idempotent mathematics (calculus) in the sense of V.P. Maslov and his collaborators. The basic paradigm is expressed in terms of an idempotent correspondence principle. This principle is similar to N. Bohr's correspondence principles in Quantum Physics (and closely related to it). A systematic application of the idempotent correspondence principle leads to a variety of results, often quite unexpected (e.g., the Legendre transform is a tropical version of the Fourier transform). As a result, in parallel with the traditional mathematics, its "classical shadow" appears.

Thursday, March 31, 2011

Posted March 21, 2011

3:40 pm - 4:30 pm Lockett 277

Igor Verbitsky, University of Missouri-Columbia Curators' Professor
Hessian Sobolev inequalities, $k$-convex functions, and the fractional Laplacian

The abstract can be found here.

Thursday, April 14, 2011

Posted March 22, 2011

3:40 pm - 4:30 pm Lockett 277

Tadele Mengesha, Louisiana State University
Global estimates for nonlinear elliptic equations over nonsmooth domains

In this talk we discuss new global regularity estimates for solutions to a class of nonlinear elliptic boundary value problems over nonsmooth domains. The nonlinear coefficients are allowed to be discontinuous but assumed to have a small mean oscillation. The boundary of the domain may be nonsmooth but sufficiently flat in the sense of Reifenberg. The main regularity estimates obtained are in weighted Lorentz spaces. As an application, these estimates will be used to obtain other regularity results in Lorentz-Morrey, Morrey, and Holder spaces. This is joint work with Phuc Nguyen.

Thursday, August 25, 2011

Posted August 4, 2011

3:40 pm - 4:30 pm Lockett 284

Paul Smith, University of Washington
Penrose tilings of the plane and noncommutative algebraic geometry

Abstract: The space X of Penrose tilings of the plane has a natural
topology on it. Two tilings are equivalent if one can be obtained from the
other by a translation. The quotient topological space X/~ is bad: every
point in it is dense. The doctrine of non-commutative geometry is to
refrain from passing to the quotient and construct a non-commutative
algebra that encodes some of the data lost in passing to X/~. In this
example (see Connes book for details) the relevant non-commutative algebra
is a direct limit of products of matrix algebras. We will obtain this
non-commutative algebra by treating the free algebra on two variables x
and y modulo the relation y2=0 as the homogeneous coordinate ring of a
non-commutative curve. The category of quasi-coherent sheaves on this
non-commutative curve is equivalent to the module category over a simple
von Neumann regular ring. That von Neumann regular ring is the same as the
direct limit algebra that Connes associates to X/~. We will discuss
algebraic analogues of various topological features of X/~. For example,
the non-vanishing of extension groups between simple modules is analogous
to the fact that every point in X/~ is dense (which is analogous to the
fact that any finite region of one Penrose tiling appears infinitely often
in every other tiling).

Thursday, September 1, 2011

Posted August 19, 2011

3:40 pm - 4:30 pm Lockett 235

Artem Pulemotov, University of Chicago
The prescribed Ricci curvature problem

We will discuss the problem of finding a Riemannian metric with given Ricci curvature on a compact manifold M. This problem has been intensively studied by mathematicians since the early 1980's.

It is partially resolved in the case where M is a closed manifold, but almost completely unresolved on manifolds with boundary. In the first part of the talk, we will review the history of the subject. After that, our focus will be on new results regarding the situation where M is a solid torus.

Thursday, October 20, 2011

Posted August 23, 2011

3:40 pm - 4:30 pm Lockett 284

Angela Pasquale, University of Metz and CNRS
Ramanujan's Master Theorem for Riemannian symmetric spaces

The abstract for this talk can be found at www.math.lsu.edu/~morales/colloquium/pasquale.pdf

Thursday, October 27, 2011

Posted September 13, 2011

3:40 pm - 4:30 pm 235 Lockett

Effie Kalfagianni, Michigan State University
Geometric and combinatorial knot invariants

Abstract: It has been known since the 80's that knot complements admit geometric decompositions and that the class of hyperbolic knots is the richest class of knots. In practice, knots are often given in terms of combinatorial topological descriptions, and it is both natural to seek for ways to deduce geometric information from these descriptions. On the other hand, in the last couple of decades ideas from physics have led to powerful and subtle combinatorial knot invariants such as the Jones knot polynomials. Understanding the relation of the combinatorial knot descriptions and invariants to the detailed structures coming from the geometric picture is an important goal of low dimensional topology that received particular attention in recent years.

In this talk I will survey some conjectured and some established such relations.

Thursday, February 2, 2012

Posted January 28, 2012

3:40 pm - 4:30 pm Lockett 277

David Vela-Vick, Columbia University
Contact structures, Legendrian and transverse knots, and Heegaard Floer homology

Abstract: The past decade has ushered in a number of major advances in the field of 3-dimensional contact geometry. Beginning with Ozsvath and Szabo's construction of an invariant of contact structures on closed 3-manifolds, a complex tapestry of generalizations and applications has emerged. In this talk, I plan to survey Heegaard Floer theory as it applies to the study of Legendrian and transverse knots. In doing so, I will discuss some surprising relationships between seemingly distinct specializations of this general theory.

Monday, February 6, 2012

Posted January 31, 2012

3:40 pm - 4:30 pm Lockett 277

Jian Song, Rutgers University
Feynman-Kac formula

Abstract: In this talk, I will review the classical Feynman-Kac formula for partial differential equations (PDEs), and explain the Feynman-Kac formulas we have obtained for stochastic partial differential equations (SPDEs).

Monday, February 13, 2012

Posted February 1, 2012

3:40 pm - 4:30 pm Lockett 277

Artem Pulemotov, University of Chicago
Geometric flows on manifolds with boundary

Abstract: Geometric flows are partial differential equations that describe evolutions of geometric objects. They are typically used to tackle problems in topology, mathematical physics, and several other fields. The canonical example of a geometric flow is the heat equation on a Riemannian manifold. In the first part of the talk, we will discuss the fundamental features of this equation. We will also speak about two estimates for its positive solutions on manifolds with boundary. A more contemporary example of a geometric flow is the Ricci flow for a Riemannian metric. It is mostly famous for its role in the proof of the Poincare conjecture. The second part of the talk will be devoted to the main features and the behavior of the Ricci flow on manifolds with boundary. Towards the end, we will give a brief overview of related problems.

Thursday, February 16, 2012

Posted January 31, 2012

3:40 pm - 4:30 pm Lockett 277

Betsy Stovall, University of California Los Angeles
Counteracting flatness with affine arclength measure

Abstract: There are many operators in harmonic analysis for which the curvature of some underlying manifold plays a significant role. We will discuss recent efforts to establish uniform estimates for such operators by compensating for degeneracies of curvature with an appropriate measure. We will focus on the case when the underlying manifolds are polynomial curves.

Tuesday, February 28, 2012

Posted February 20, 2012

3:40 pm - 4:30 pm Lockett 277

Ling Long, Iowa State University
The arithmetic of modular forms for noncongruence subgroups

Abstract: Among all finite index subgroups of the modular group, majority of them are noncongruence, i.e. they cannot be described in terms of congruence relations. Compared to the classical theory of congruence modular forms, modular forms for noncongruence subgroups are more mysterious due to the lack of efficient Hecke theory. However, noncongruence modular forms exhibit some remarkable properties and are closely related to many topics in number theory. In this talk, we will introduce these functions and discuss some recent developments in this area. In particular, we will consider Galois representations attached to noncongruence modular forms constructed by Tony Scholl which are generalizations of Deligne's Galois representations attached to classical Hecke eigenforms. We will prove under special circumstances that these Scholl representations are automorphic in the sense that their L-functions agree with the L-functions of automorphic forms on reductive groups and then give some applications of such automorphic results.

Thursday, March 8, 2012

Posted February 27, 2012

3:40 pm - 4:30 pm Lockett 277

Christopher Bremer, Mathematics Department, LSU
A new perspective on flat G-bundles and the Stokes phenomenon

Let G/C be a reductive algebraic group and let X/C be a smooth (not necessarily compact) algebraic curve. Flat G-bundles on X are a natural generalization of differential equations with algebraic coefficients, where the latter are viewed as vector bundles (having structure group GL_n) equipped with an integrable connection that is meromorphic at infinity. When the connection has an irregular singular point, the asymptotic series of a fundamental solution jumps discontinuously as it is continued across sectors in a neighborhood of that point. This behavior is known as the Stokes phenomenon. The "jumps" are encoded by elements of the group G, so one might think of the Stokes data as being an enhancement of the monodromy representation associated to a meromorphic differential equation.
The wild ramification case of the geometric Langlands conjecture suggests that there should be a natural correspondence between Stokes data arising from the irregular monodromy map, and representation theoretic data associated to the Langlands dual of the loop group. I will discuss a new approach (based on joint work with D. Sage) to the study of irregular flat G-bundles, inspired by methods from p-adic representation theory. Specifically, we have developed a geometric version of the Moy-Prasad theory of fundamental strata (aka minimal K-types). In this talk I will explain how the theory of fundamental strata applies to the study of moduli spaces of flat G-bundles, allowing one to significantly generalize results of Boalch, Jimbo et al., and others on the Stokes map and the irregular isomonodromy equations.

Thursday, March 15, 2012

Posted October 27, 2011

3:40 pm - 4:30 pm Lockett 277

Abhinav Kumar, Massachusetts Institute of Technology
Lattices, sphere packings and spherical codes

Abstract: It is a classical problem in geometry to find the densest arrangement of non-overlapping spheres in Euclidean space. I will give a brief overview of sphere packing and related geometrical problems, like the kissing number problem. After surveying some of the known results, I'll describe recent approaches to these problems, involving linear programming bounds, numerical optimization using gradient descent, and deformations and the notion of rigidity. The talk will also focus on many concrete examples and explain what we are able to observe and prove using these techniques, as well as many natural open questions.

Thursday, March 22, 2012

Posted January 29, 2012

3:40 pm - 4:30 pm Lockett 277

Kenneth Gross, University of Vermont
Special Functions of Matrix Argument

Classical special functions such as the gamma function, Bessel functions, and hypergeometric functions, to name a few, apply in many different contexts ranging from mathematical analysis to statistics and the physical sciences. Beginning over six decades ago, generalizations of such classical functions to spaces of matrices (and to symmetric cones more generally) arose in the context of harmonic analysis, multivariate statistics, number theory, and the representation theory of Lie groups. In this talk, expository in nature, we will discuss the origins of these generalizations, highlight the critical role of symmetry considerations, and touch upon applications which have appeared recently in multiple-input multiple-output (MIMO) models that form the basis of modern cell-phone transmission.

Thursday, March 29, 2012

Posted February 23, 2012

3:40 pm - 4:30 pm Lockett 277

Aaron Welters, LSU
Dissipative Properties of Systems Composed of High-Loss and Lossless Components

Abstract: We study energy dissipation features of a system composed from lossy and lossless components. One of the principal result is that the dissipation causes modal dichotomy, i.e., splitting of the eigenmodes into two distinct classes according to their dissipative properties: high-loss and low-loss modes. Interestingly, larger losses in the lossy component make the entire composite less lossy, the dichotomy more pronounced, low-loss modes less lossy, and high-loss modes less accessible to external excitations. We also have carried out an exhaustive analytical study of the system quality factor. This is joint work with Alexander Figotin.

Thursday, April 19, 2012

Posted August 23, 2011

3:40 pm - 4:30 pm Lockett 277

Benson Farb, University of Chicago
Permutations and polynomiality in algebra and topology

Abstract: Tom Church, Jordan Ellenberg and I recently discovered that each Betti number of the space of configurations on n points on any manifold is a polynomial in n. Similarly for the moduli space of n-pointed genus g curves. Similarly for the dimensions of various spaces of homogeneous polynomials arising in algebraic combinatorics. Why? What do these disparate examples have in common? The goal of this talk will be to answer this question by explaining a simple underlying structure shared by these (and many other) examples in algebra and topology.

Thursday, September 13, 2012

Posted September 10, 2012

3:30 pm - 4:20 pm Lockett 277

Michael Malisoff, LSU
Adaptive Tracking and Parameter Identification for Nonlinear Control Systems

Given a control system that has a vector of unknown constant parameters and a reference trajectory for the system, the adaptive tracking and parameter identification problem is to find a dynamic controller that forces the system to track the reference trajectory and a parameter estimator that converges to the unknown parameter vector. In the first part of this talk, I will review the necessary background on control theory. Then I will discuss my research on adaptive tracking and parameter identification for systems with unknown control gains. In the last part, I will discuss an application to marine robots and open problems. This work is joint with Frederic Mazenc and Fumin Zhang. This talk will be understandable to anyone who knows all of the material in the basic graduate ODEs course Math 7320 at LSU.

Thursday, October 4, 2012

Posted August 22, 2012

3:30 pm - 4:20 pm Locket 277

Joseph Wolf, University of California, Berkeley
Infinite Dimensional Lie Groups

Abstract: I'll survey some analytic aspects of a class of infinite dimensional
Lie groups that have a lot of properties in common with their finite
dimensional counterparts. These include smoothness, the Borel-Weil
and Bott-Borel Weil theorems, and the possibility of extending some
of Harish-Chandra's constructions from the finite dimensional case.
This leads to a number of interesting open problems.

Thursday, October 11, 2012

Posted September 11, 2012

3:30 pm - 4:20 pm Lockett 277

Barbara Rüdiger, Bergische Universität Wuppertal - Germany
Stochastic (Partial) Differential Equations with Lévy noise: Existence, uniqueness and properties of solutions.

Abstract: In this talk we first analyze properties of integrands when integration is done with respect to Lévy processes or compensated Poisson random measures. Then we introduce SP(D)Es with Lévy noise and show the existence, uniqueness and continuous properties of the solutions.

Thursday, October 25, 2012

Posted September 11, 2012

3:30 pm - 4:20 pm Lockett 277

Aderemi Kuku, Grambling State University William W.S. Clayton Endowed Professor of Mathematics
Higher Algebraic K-Theory and Representations of Algebraic Groups

In this talk, I at first discuss some features of K-theory as a multidisciplinary subject that classifies various mathematical structures and objects as well ramifies into and co-ordinates several areas of mathematics. Next, I present constructions and computations of equivariant higher K-theory and profinite (continuous) equivariant higher K-theory for the action of algebraic groups with applications to twisted flag varieties.

A more detailed abstract can be found here.

Thursday, November 8, 2012

Posted September 11, 2012

3:30 pm - 4:20 pm Lockket 277

Yang Tonghai, University of Wisconsin
The Gross-Zagier formula -- history, application, and development

Abstract: How do you know whether a cubic equation like $y^2 =x^3 -n^2 x$ have infinitely many solutions or not (for a fixed integer $n$)? How do you find them? The Birch and Swinnerton-Dyer conjecture would tell you that some analysis ($L$-function) would tell you a lot about this kind of questions. The Gross-Zagier formula gives a deep and direct relation between the arithmetic and analysis. In this talk, I will briefly talk about this beautiful formula, some of its significant applications, and its generalizations.

Tuesday, November 20, 2012

Posted November 12, 2012

3:30 pm - 4:20 pm Lockett 277

Renzo Cavalieri, Colorado State University
Polynomiality and Wall Crossings in Hurwitz Theory

Abstract: in this talk I will present a story that began with the observation of Goulden-Jackson-Vakil that families of Hurwitz numbers tend to have interesting polynomiality or piecewise-polynomiality aspects. Cavalieri-Johnson-Markwig subsequently exploited the combinatorics suggested by tropical geometry in order to gain a good understanding of this phenomena, and to be able to describe wall crossings. The story is now evolving with an attempt of lifting these observations from the level of "numbers" to the level of "cycles". Again, the parallel with tropical geometry helps shed light on the combinatorial features of certain families of Hurwitz classes. The story is understood so far in genus 0 and becomes substantially more complicated in higher genus. The most recent work discussed is joint work with Aaron Bertram and Hannah Markwig.

Thursday, January 24, 2013

Posted December 22, 2012

3:30 pm - 4:20 pm 277 Lockett

Tai Melcher, University of Virginia
Smoothness properties for some infinite-dimensional heat kernel measures

Abstract: Smoothness is a fundamental principle in the study of measures on
infinite-dimensional spaces, where an obvious obstruction to overcome is
the lack of an infinite-dimensional Lebesgue or volume measure. Canonical
examples of smooth measures include those induced by a Brownian motion,
both its end point distribution and as a real-valued path. Heat kernel
measure is the law of a Brownian motion on a curved space, and as such is
the natural analogue of Gaussian measure there. We will discuss some
recent smoothness results for these measures on certain natural classes of
infinite-dimensional groups, including in some degenerate settings. This
is joint work with Fabrice Baudoin, Daniel Dobbs, and Masha Gordina.

Thursday, March 7, 2013

Posted September 11, 2012

3:30 pm - 4:20 pm Lockett 277

Nicholas Ercolani, University of Arizona
Conservation Laws in Random Matrix Theory

ABSTRACT: Analytical Combinatorics is an old subject (going back at least to Euler) which has received renewed impetus from several directions including complex systems theory, large scale computation, quantum gravity and non-equilibrium statistical mechanics. In particular methods from nonlinear PDE theory, both deterministic and stochastic, have begun to play a significant role in advancing this classical subject. In this talk we will discuss some very recent developments that bring to bear methods for studying systems of conservation laws on the asymptotic analysis of generating functions for "maps". A "random map" is a random topological tessellation of a Riemann surface. These are combinatorial objects that first arose in attempts to solve the four color problem but soon thereafter took on a life of their own. Subsequently, physicists working on the unification of the "strong" and "weak" forces discovered that generating functions for maps emerge naturally in the enumeration of Feynman diagrams for random unitary matrix ensembles. Our recent work provides the means for the explicit evaluation of map generating functions in terms of closed form solutions of the aforementioned conservation laws. These conservation laws are certain continuum limits of the Toda lattice differential equations in which the time variables are coupling coefficients of the random matrix ensembles. This topic brings together many areas of pure and applied mathematics and we will describe some of these bridges.

Friday, March 15, 2013

Posted December 22, 2012

3:30 pm - 4:20 pm Lockett 285

Julian Hook, Indiana University, Bloomington
Graph Theory and the Musical Tonnetz

Note: This colloquium is held on a Friday.

Thursday, March 21, 2013

Posted February 27, 2013

3:30 pm - 4:20 pm Lockett 277

Ilya Spitkovsky, College of William and Mary
The current state of the almost periodic factorization

Factorization of matrix functions (that is, their representation as products of multiples analytic inside and outside the given closed curve) arises naturally in many applications, including those to convolution type equations on a half-line (the classical Wiener-Hopf method). As it happens, the equations on finite intervals also can be treated via the factorization method. The resulting matrix functions, however, are of oscillating type, which has not been treated until recently. The general case can be boiled down to the situation when the matrix is almost periodic, that is, its elements belong to the algebra generated by exp(iax) with real values of the parameter a. We will discuss the current state of the factorization problem for such matrices. A special attention will be paid to a (seemingly narrow) case of 2-by-2 triangular matrix functions, but even for them the factorability properties remain a mystery. in striking difference with both the scalar almost periodic case and the classical Wiener-Hopf setting.

Thursday, April 11, 2013

Posted December 22, 2012

3:30 pm - 4:20 pm Lockett 277

Sam Nelson, Claremont McKenna College
Enhancements of Counting Invariants

Abstract: Counting invariants are among the simplest computable invariants of knots and links. In this talk we will see various strategies for enhancing and strengthening counting invariants and some connections between these invariants and other knot and link invariants.

Tuesday, May 14, 2013

Posted May 7, 2013

3:30 pm Lockett 277

Arithmetic invariants: From finite groups to modular categories

Richard Ng, Iowa State University, visiting Cornell University

Thursday, May 16, 2013

Posted May 10, 2013

8:30 am Johnston Hall 338 (Training Room)

Around Lusztig's conjecture: Arithmetic problems in representation theory, combinatorics and geometry.

Peter Fiebig, Erlangen University, Germany will present a "virtual colloquium"

The early time 8:30 AM is to accommodate the 7-hour time difference between here and Germany.

Tuesday, September 3, 2013

Posted August 28, 2013

3:30 pm - 4:20 pm Lockett 285

Phuc Nguyen, Department of Mathematics, Louisiana State University
Capacities, nonlinear Calderón-Zygmund theory, and PDEs with power nonlinearities

We discuss the solvability of fully nonlinear and quasilinear equations of Lane-Emden type, quasilinear equations of Riccati type, and stationary Navier-Stokes equations with strongly singular external forces. Complete characterizations of existence will be given in connection with the theory of capacities, weighted norm inequalities, and a nonlinear version of Calderón-Zygmund theory for singular integrals. Removable singularities of Lane-Emden type equations will be described along with the stability of the stationary Navier-Stokes equation. This talk is based on joint work with Igor E. Verbitsky, Tadele Mengesha, and Tuoc Van Phan.

Thursday, September 12, 2013

Posted August 27, 2013

3:30 pm Lockett 285

Oliver T. Dasbach, Mathematics Department, LSU
Knots, hyperbolic volume, and q-series

There will be refreshments in the Keisler lounge at 3 pm

Tuesday, September 17, 2013

Posted August 27, 2013

3:30 pm Lockett 285

Stephen Shipman, Mathematics Department, LSU
Embedded Eigenvalues and Resonance in Quantum Graphs

A locally perturbed periodic graph operator admits bands of continuous spectrum as well as discrete eigenvalues corresponding to defect states. Under generic conditions, the eigenvalues lie in the gaps between the spectral bands. The obstruction to eigenvalues embedded in the continuous spectrum is algebraic--namely, that a generic polynomial in several variables does not factor. The polynomial in question comes from the Floquet transform of the operator; its zero set, called the Fermi surface, describes the admissible quasi-momenta for a given energy. I will show that there is an interesting class of quantum graphs possessing symmetries that allow the Fermi surface to separate for all frequencies. This separation allows one to construct embedded eigenvalues that result in complex resonant scattering when excited by radiation states of the surrounding continuous spectrum.

There will be refreshments in the Keisler lounge at 3 pm.

Thursday, September 19, 2013

Posted August 27, 2013

3:30 pm Lockett 285

Hongchao Zhang, Louisiana State University
Recent Advances on Gradient Methods in Nonlinear Optimization

Abstract: In this talk I would briefly talk about some recently developed gradient-based algorithms for smooth unconstrained optimization, for smooth and nonsmooth composite optimization, for optimization with inexact gradients, and for general smooth nonlinear programming. The convergence properties as well as practical performance of some of these algorithms will be discussed in this talk.

There will be refreshments in the Keisler lounge at 3pm

Tuesday, September 24, 2013

Posted August 27, 2013

3:30 pm Lockett 285

Blaise Bourdin, Department of Mathematics, Louisiana State University
The variational approach to fracture: recent developments and extensions.

Most models for the fracture of brittle materials rely on an energetic argument, the celebrated Griffith criterion, combined with ad-hoc branching criteria. In addition, such models rely heavily on smoothness and regularity assumptions whose validity is debatable. The variational approach to fracture was developed as an extension of Griffith criterion preserving its essence, competition between surface and volume energy, while avoiding any ad-hoc branching criterion or regularity hypothesis of fracture sets, in space or time. It is formulated as a sequence of unilateral global minimization problems of a free discontinuity energy. I will first recall some elements of the mathematical analysis of this approach. I will then describe its numerical implementation, focusing on methods based on elliptic regularization. I will finally show how this approach can be used in many applications, including transverse fracture and debonding of thin films, drying of colloidal suspension, thermal shocks of glass and ceramics, dynamic fracture and hydraulic stimulation. I will describe the mathematical and algorithmic tools developed for each specific problem, and present validation and verification experiments.

There will be refreshments in the Keisler lounge at 3 pm

Thursday, September 26, 2013

Posted August 27, 2013

Lockett 285

Pallavi Dani, Department of Mathematics, LSU
Filling invariants for groups

Any finitely generated group can be endowed with a natural metric which is unique up to maps of bounded distortion, i.e. quasi-isometries. A central question in geometric group theory is to classify finitely generated groups up to quasi-isometry. I will talk about recent work on understanding quasi-isometry invariants for groups in various settings, with an emphasis on filling invariants, a class of invariants that are motivated by classical isoperimetric inequalities.

There will be refreshments in the lounge at 3 pm

Thursday, October 24, 2013

Posted October 14, 2013

3:30 pm Lockett 285

Siu-hung (Richard) Ng, LSU
Frobenius-Schur indicators and exponents

ABSTRACT: Frobenius-Schur indicators were introduced a century ago for the representations of finite groups. It has been proved recently that these indicators are invariants of tensor categories, and so are the exponents of finite groups. In this talk, we will discuss dimensions, exponents and indicators for finite groups, and their generalizations in the settings of Hopf algebras as well as tensor categories.

There will be refreshments in the Keisler lounge at 3 PM

Thursday, October 31, 2013

Posted October 14, 2013

3:30 pm - 4:20 pm Lockett 285

Tadeusz Iwaniec, Syracuse University
Sobolev mappings and energy integrals in nonlinear elasticity

The abstract for this talk can be downloaded here.

Thursday, November 14, 2013

Posted October 9, 2013

3:30 pm - 4:20 pm Lockett 285

Gregor Masbaum, CNRS, Institut de Mathematiques de Jussieu, Paris, France
All finite groups are involved in the mapping class group

Abstract: A (finite) group G is said to be involved in an (infinite) group Gamma if G is isomorphic to a quotient of a subgroup of Gamma of finite index. I will discuss examples and non-examples of groups Gamma with the property that every finite group is involved in Gamma. I will then describe my joint work with A. Reid where we show that mapping class groups of surfaces have this property. A remarkable feature of the proof is that it involves quantum topology. In fact, the proof uses precisely the Integral TQFT-representations of mapping class groups that P. Gilmer and I constructed some years ago. However, no previous knowledge of quantum topology will be assumed in this talk.

Thursday, November 21, 2013

Posted October 9, 2013

3:30 pm Lockett 285

Ravi Rau, Department of Physics and Astronomy, LSU
Quantum spins, real rotations, and a 1913 Ramanujan conjecture

Abstract: Quantum states are defined as complex variables and their time evolution is given by unitary transformations. For a quantum spin-1/2 or qubit of the field of quantum information, an equivalent picture of the Bloch sphere and real rotations of a unit vector from the origin to a point on the sphere has proved enormously useful. Extension of this nice geometrical view is also possible for a pair of qubits, such pairs being the fundamental objects of interest for entanglement and other quantum correlations that are used in quantum computing, key distribution and teleportation. The above results rest on the homeomorphism of SU(2)-SO(3) and SU(4)-SO(6) group pairs. These will be discussed and a hundred-year old conjecture of number theory (later the Ramanujan-Nagell Theorem) used to show that no such correspondence between unitary evolution and real rotations is available for systems of more qubits. However, the general construction of the evolution operator for SU(N) and of some of its sub-groups are likely to be of interest throughout the field of quantum information.

Thursday, January 23, 2014

Posted January 9, 2014

3:30 pm - 4:20 pm Lockett 285

Karl-Hermann Neeb, Universität Erlangen-Nürnberg
Reflection positivity and unitary Lie group representations

Reflection positivity (sometimes called Osterwalder-Schrader positivity) was introduced by Osterwalder and Schrader in the context of axiomatic euclidean field theories. On the level of unitary representations, it provides a passage from representations of the euclidean isometry group to representations of the Poincaré group. In our talk we shall explain how these ideas can be used to obtain a natural context for the passage from representations of Lie groups with an involutive automorphism (symmetric Lie groups) to representations of their dual Lie group. Already the case of one-parameter groups is of considerable analytic interest.

Thursday, January 30, 2014

Posted January 9, 2014

3:30 pm - 4:20 pm Lockett 285

Tom Lenagan, University of Edinburgh
Totally nonnegative matrices

A real matrix is totally nonnegative if each of its minors is nonnegative, and is totally positive if each minor is greater than zero. We will outline connections between the theory of total nonnegativity and the torus invariant prime spectrum of the algebra of quantum matrices, and will discuss some new and old results about total nonnegativity which may be obtained using methods derived from quantum matrix methods. Most of the material is joint work with Stephane Launois and Ken Goodearl. (You don't need to know anything about quantum matrices to follow this talk.)

Thursday, February 27, 2014

Posted January 9, 2014

3:30 pm - 4:20 pm Lockett 285

Satyan Devadoss, Williams College and Stanford University
Combinatorics of Surface Deformations

In the 1970s, Deligne and Mumford constructed a way to keep track of particle collisions using Geometric Invariant Theory. These spaces were then utilized by Gromov and Witten as invariants arising from string field theory and quantum cohomology. Later, Kontsevich and Fukaya generalized these ideas when studying deformation quantization to include surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds.

We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface, relating it to the well-known phenomenon of bubbling. Our main result classifies all such spaces that can be realized as convex polytopes. A new polytope is introduced based on truncations of cubes, and its combinatorial and algebraic structures are related to generalizations of the classical associahedron.

Thursday, March 27, 2014

Posted March 19, 2014

3:30 pm - 4:20 pm Lockett 285

Stefan van Zwam, LSU
Beyond Total Unimodularity

A matrix is totally unimodular if the determinant of each square submatrix is in {-1, 0, 1}. Such matrices are a cornerstone of the theory of integer programming, and they have been studied extensively. In the late '90s, Whittle introduced several classes of matrices with similar properties: the determinants of the submatrices are restricted to a certain set. In this talk I will discuss some results from the theory of totally unimodular matrices, and outline which of those results will, won't, or might generalize to Whittle's classes. The natural context for these problems is matroid theory, but prior knowledge of matroids is not required for this talk.

Thursday, April 10, 2014

Posted February 25, 2014

3:30 pm Business Education Complex (BEC) 1510

Jean-Pierre Serre, College de France, emeritus Fields Medal recipient, Abel Prize recipient, and many more
Trace Forms

Refreshments will be served in the Keisler lounge from 2:45 to 3:15 pm. It takes approximately ten minutes to walk from Lockett Hall to BEC where the colloquium will be given.

Thursday, May 1, 2014

Posted January 13, 2014

3:30 pm - 4:20 pm Lockett 285

Melvin Leok, University of California, San Diego
Lie group and homogeneous variational integrators and their applications to geometric optimal control theory

The geometric approach to mechanics serves as the theoretical underpinning of innovative control methodologies in geometric control theory. These techniques allow the attitude of satellites to be controlled using changes in its shape, as opposed to chemical propulsion, and are the basis for understanding the ability of a falling cat to always land on its feet, even when released in an inverted orientation.

We will discuss the application of geometric structure-preserving numerical schemes to the optimal control of mechanical systems. In particular, we consider Lie group variational integrators, which are based on a discretization of Hamilton's principle that preserves the Lie group structure of the configuration space. In contrast to traditional Lie group integrators, issues of equivariance and order-of-accuracy are independent of the choice of retraction in the variational formulation. The importance of simultaneously preserving the symplectic and Lie group properties is also demonstrated.

Recent extensions to homogeneous spaces yield intrinsic methods for Hamiltonian flows on the sphere, and have potential applications to the simulation of geometrically exact rods, structures and mechanisms. Extensions to Hamiltonian PDEs and uncertainty propagation on Lie groups using noncommutative harmonic analysis techniques will also be discussed.

We will place recent work in the context of progress towards a coherent theory of computational geometric mechanics and computational geometric control theory, which is concerned with developing a self-consistent discrete theory of differential geometry, mechanics, and control.

This research is partially supported by NSF CAREER Award DMS-1010687 and NSF grants CMMI-1029445, DMS-1065972, and CMMI-1334759.

Thursday, September 4, 2014

Posted August 26, 2014

3:30 pm Lockett 241 (refreshments in the lounge at 3:00)

Ling Long, Mathematics Department, LSU
Hypergeometric functions and some recent applications in number theory

Abstract: Hypergeometric functions, which are solutions of ordinary differential equations with only 3 regular singularities, are an important class of special functions. Hypergeometric functions are very useful for several subjects such as combinatorial identities, triangle groups, modular forms, and algebraic varieties. In this talk, we will give a general introduction to hypergeometric functions and discuss some recent applications in number theory.

Wednesday, September 10, 2014

Posted August 26, 2014

3:30 pm - 4:20 pm 235 Lockett

Xiaoliang Wan, Louisiana State University
Some numerical issues about quantifying the effects of uncertainty

Abstract: The role of uncertainty in mathematical models has received more attention in the last two decades due to the quick development of algorithms and computation capability. In this talk I will discuss numerical computation for three cases to quantify the effects of uncertainty, including parametric uncertainty, stochastic modeling based on Wick product and minimum action method for large deviation principle, where I will focus on the last case. I will describe some recent progress of minimum action method and its application to model the nonlinear instability of wall-bounded shear flows as a rare event.

Thursday, September 18, 2014

Posted August 26, 2014

3:30 pm - 4:30 pm Lockett 241

Scott Baldridge, Louisiana State University
Using a discrete set of transformations to prove smooth invariants of embedded tori in R^n

Abstract: It has been well known for over 80 years that knots in R^3 can be represented by 2-dimensional knot diagrams, and that three Reidemeister moves on those diagrams could be used to understand and prove invariants of knots. The problem with 2-dimensional diagrams is that smooth invariants that rely on metrics, differential forms, curvature forms, differential equations, etc. cannot be defined nor checked using the 2-dimensional moves. Motivated by search for a "Reidemeister-like" set of moves for embedded surfaces in R^4 (using actual embeddings, not projections), I recently developed the notion of a cube diagram to represent embedded n-tori in R^(n+2). In the case of knots in R^3, we proved that any cube diagram of a knot can be obtained from any other cube diagram of the knot using 2 types of cube diagram moves; this theorem allows us to prove differential topology invariants of knots in R^3 using a discrete set of transformations of the knot. In this talk, I will describe some differential topology applications of cube diagrams to Chern-Simons theory, and (if time) to higher dimensional embeddings.

Monday, September 22, 2014

Posted August 27, 2014

3:30 pm - 4:20 pm Lockett 241

Yaniv Almog, Department of Mathematics, LSU
A Rigorous Proof of the Maxwell-Claussius-Mossotti Formula

Abstract: We consider a large number of identical inclusions (say spherical), in a bounded domain, with conductivity different than that of the matrix. In the dilute limit, with some mild assumption on the first few marginal probability distribution (no periodicity or stationarity are assumed), we prove convergence in H1 norm of the expectation of the solution of the steady state heat equation, to the solution of an effective medium problem, which for spherical inclusions is obtained through the Maxwell-Clausius-Mossotti formula. Error estimates are provided as well.

Thursday, October 9, 2014

Posted September 15, 2014

3:30 pm - 4:20 pm Lockett 241

Susan Montgomery, University of Southern California
Orthogonal Representations: From Groups to Hopf Algebras

The abstract for this talk is available here .

Thursday, October 23, 2014

Posted September 4, 2014

3:30 pm - 4:20 pm Lockett 241

Victor Moll, Department of Mathematics, Tulane University
The evaluation of definite integrals

Abstract: The question of finding out a closed-form of a definite integral has its origin with Calculus itself. In spite of many advances, the algorithmic question is still not completely resolved. This talk will present a variety of such evaluations that lead to interesting connections to Number Theory, Combinatorics and (naturally) Special Functions.

Thursday, November 20, 2014

Posted October 30, 2014

3:30 pm - 4:20 pm Lockett 241

James Zhang, University of Washington
Zariski cancellation problem for noncommutative algebras

Abstract: The famous Zariski cancellation problem asks if the polynomial algebra of more than two variables is cancellative. We consider a noncommutative version of the cancellation problem and obtain an affirmative answer for many classes of noncommutative algebras. Joint work with Jason Bell.

Thursday, December 4, 2014

Posted October 2, 2014

3:30 pm - 4:40 pm

F. Alberto Grünbaum, University of California, Berkeley
Time and band limiting and the bispectral problem: motivation, applications and open problems.

Abstract: The problem of how to best use (noisy) partial spectral information to determine a signal of finite duration starts with the work of C. Shannon, D. Slepian, H. Landau and H. Pollak at Bell Labs back around 1960. I will tell parts of this story as well as the way in which it led to the bispectral problem. The mathematics behind the bispectral problem is much richer than one may suspect: integrable systems like KdV, isomonodromic deformations, characters of representations of certain groups, certain non-commutative algebras of matrix valued differential operators, contacts with random matrix theory and other gems are all pieces of this puzzle. I am very interested in making this a two-way street in terms of finding bispectral situations that lead to the "time-band limiting" miracle of Slepian, Landau and Pollak in terms of finding a commuting differential operator for a naturally appearing integral one. This ongoing effort involves the work of several people, including Milen Yakimov.

Thursday, January 22, 2015

Posted January 9, 2015

3:30 pm - 4:20 pm Lockett 285

Arnab Ganguly, University of Louisville
Limit theorems in stochastic analysis

Limit theorems for stochastic processes have a variety of applications in diverse fields ranging from statistics to biology. While the weak convergence results often help to identify approximate continuous models from discrete-time ones, the results in the form of moderate and large deviations help to assess the quality of the approximations by studying various 'rare events'. The talk will focus on some systematic approaches to limit theorems for stochastic differential equations, which are particularly beneficial in infinite-dimensional settings. Several specific examples will be discussed illustrating the usefulness of these approaches.

Thursday, January 29, 2015

Posted January 9, 2015

3:30 pm - 4:20 pm Lockett 285

Lingjiong Zhu, University of Minnesota
Self-Exciting Point Processes

Self-exciting point processes are simple point processes that have been widely used in neuroscience, sociology, finance and many other fields. In many contexts, self-exciting point processes can model the complex systems in the real world better than the standard Poisson processes. We will discuss the Hawkes process, the most studied self-exciting point process in the literature. We will talk about the limit theorems and asymptotics in different regimes. Extensions to Hawkes processes and other self-exciting point processes will also be discussed.

Thursday, February 5, 2015

Posted January 9, 2015

3:30 pm - 4:20 pm Lockett 285

Eunghyun Lee, Centre de recherches mathématiques, Montréal
The Coordinate Bethe Ansatz Solvable Interacting Particle Systems

Interacting particle systems on the integer lattice that the coordinate Bethe Ansatz method can be applied to have connections to the random matrix theory and the symmetric function theory. Based on the coordinate Bethe Ansatz method, the exact formulas of the transition probabilities of the finite systems are given by the multi-dimensional contour integrals. In particular, we consider two initial configurations of the systems that are related to the GUE Tracy-Widom distribution and the GOE Tracy-Widom distribution. The combinatorial properties arising from our models are also discussed.

Thursday, February 12, 2015

Posted January 9, 2015

3:30 pm - 4:20 pm Lockett 285

Grace Wang, Duke University
Data Analysis with Low-dimensional Structures

Analyzing data collected from different fields is a challenge facing scientists and engineers. The property of being high-dimensional makes these data sets hard to investigate. Fortunately, in many cases, data locally concentrate along a low-dimensional subspace, which makes it possible to analyze. This talk will demonstrate different objectives where low-dimensional structures can be utilized for various data analysis purposes.

A major part of the talk will introduce a solution to the high-dimensional regression problem. More precisely, given a set of high-dimensional predictors {xi} and the corresponding high-dimensional responses {yi}, the high-dimensional regression problem seeks a function f such that f(xi) is sufficiently close to yi for all i. An algorithm with piecewise linear mappings built on a tree structure is proposed. It is designed to handle high-dimensional predictors and responses, and in particular, cases where closeness of predictors is inconsistent with closeness of responses. Experimental results demonstrate the excellent performance of our method.

Additional problems in the area will be discussed briefly, including the consistency analysis of a subspace-based classification algorithm and an automated J wave (anomaly) detection in heart (electrocardiography) signals.

Thursday, March 5, 2015

Posted February 10, 2015

3:30 pm - 4:20 pm 285 Lockett

Tadele Mengesha, The University of Tennessee, Knoxville
The variational convergence of some nonlocal convex functionals

Abstract: In this talk, I will discuss a class of variational problems associated with nonlocal elastic energy of peridynamic-type which result in nonlinear nonlocal systems of equations with various volumetric constraints. The well-posedness of variational problems is established via careful studies of the related energy spaces which are made up of vector-valued functions. In the event of vanishing nonlocality we establish the convergence of the nonlocal energy to a corresponding local energy via Gamma convergence. For some convex energy functionals we will explicitly find the corresponding limit energy. As a special case the classical Navier-Lame potential energy will be realized as a limit of linearized peridynamic energy offering a rigorous connection between the nonlocal peridynamic model to classical mechanics for small uniform strain.

Tuesday, March 17, 2015

Posted March 6, 2015

3:30 pm - 4:20 pm Lockett 285

Aaron Lauda, University of Southern California
Traces and diagrams on the annulus

In this talk we will explore the notion of "trace" and how it can be generalized and given a graphical description in terms of diagrams on an annulus. Extending these notions beyond vector spaces and linear maps, we will show how the notion of trace can be generalized to any situation in which an algebraic object admits a graphical description in terms of planar diagrammatics. We will explain how these ideas provide a simple and intuitive way to understand sophisticated constructions arising in "categorification" and geometric representation theory.

Thursday, March 26, 2015

Posted September 9, 2014

3:30 pm - 4:40 pm TBA

Peter Kuchment, Texas A&M
Can one hear the heat of a body? Mathematics of hybrid imaging

Medical/industrial/geophysical imaging has been for decades an amazing area of applications of mathematics, providing a bonanza of beautiful and hard problems with real world applications. One can find almost any area of math being involved there. In this talk, I will survey a recent trend of designing the so called coupled physics (or hybrid) imaging methods and mathematical problems arising there. No prior knowledge of mathematics of imaging is assumed.

Thursday, April 16, 2015

Posted October 20, 2014

3:30 pm Lockett 285

Henri Cohen, University of Bordeaux I
Number Fields, Class Groups, and Regulators.

Abstract: In this talk, I will present the main results and conjectures related to the enumeration of number fields, and to their class groups and regulators. I will in particular give the known results on the enumeration of number fields of small degree, general conjectures on the subject, known theorems on the size of the class number, and the main heuristic predictions concerning class groups. I will also mention the computational tools used to obtain data concerning these objects.

Thursday, April 30, 2015

Posted April 18, 2015

3:30 pm - 4:20 pm Lockett 285

Ruth Charney, Brandeis University
Hyperbolic-like Boundaries

Boundaries of hyperbolic spaces play an important role in the study of hyperbolic groups and hyperbolic manifolds. Analogous boundaries exist for simply connected spaces of non-positive curvature (CAT(0) spaces) but they are not as well behaved and hence less effective. I will discuss the differences between these two settings and then introduce a new boundary for a very general class of metric spaces, designed to capture hyperbolic-like behavior in non-hyperbolic spaces. (Joint work with Harold Sultan and Matt Cordes)

Thursday, September 10, 2015

Posted August 31, 2015

3:30 pm - 4:20 pm Lockett 277

Pramod Achar, Mathematics Department, LSU
Intersection cohomology and representation theory

Intersection cohomology (a variant of the usual singular cohomology) has been a powerful tool in representation theory for over 35 years, playing a role in such major developments as the proof of the Kazhdan-Lusztig conjectures. After discussing some classical applications of complex intersection cohomology through examples, I will focus on new developments that have made intersection cohomology with Z/pZ coefficients more accessible, along with applications such as the proof of the Mirkovic-Vilonen conjecture.

Thursday, September 17, 2015

Posted August 31, 2015

3:30 pm - 4:20 pm Lockett 277

Shawn Walker, LSU
Numerical Analysis For Multi-Physics Moving Interface Problems

Moving interface and free boundary problems play a critical role in many areas of mathematics, physics, and engineering (examples are surface tension/curvature-driven flows and other geometric flows). Many new computational methods have been developed in recent years to tackle these problems in the presence of other physical effects. In this talk, I will discuss modeling and numerical analysis for three areas: two-phase problems, shape optimization, and liquid crystals. I will highlight theoretical results for modeling and simulating these problems, as well as show numerical results and simulations to illustrate the methods.

Thursday, November 5, 2015

Posted September 23, 2015

3:30 pm - 4:20 pm Lockett 277

Geoffrey Mason, UC Santa Cruz
The unbounded denominator conjecture

The unbounded denominator conjecture (UBD) is a very general statement that includes as special cases both the main modular-invariance conjecture in rational conformal field theory and an old conjecture of Atkin-Swinnerton-Dyer about noncongruence modular forms. We will explain the origins of UBD, its connections with the Fuchsian theory of linear differential equations, and how it can be proved in low dimensions. The talk is aimed at a general audience -- no special expertise required.

Monday, February 1, 2016

Posted January 29, 2016

3:30 pm - 4:20 pm Lockett 285

Brian Street, University of Wisconsin-Madison
The Frobenius Theorem

We present a quantitative version of the classical Frobenius theorem from differential geometry. This theorem can be seen as providing scaling maps which can be used to study a range of problems in analysis. We present two such applications: a theory of singular Radon transforms (joint with E. M. Stein) and a theory of multi-parameter singular integrals which has applications to PDEs and several complex variables.

Friday, February 5, 2016

Posted January 29, 2016

1:30 pm - 2:20 pm Lockett 241

Jing Tao, University of Oklahoma
Stable commutator lengths in right-angled Artin groups

The commutator length of an element g in the commutator subgroup [G,G] of a group G is the smallest k such that g is the product of k commutators. When G is the fundamental group of a topological space, then the commutator length of g is the smallest genus of a surface bounding a homologically trivial loop that represents g. Commutator lengths are notoriously difficult to compute in practice. Therefore, one can ask for asymptotics. This leads to the notion of stable commutator length (scl) which is the speed of growth of the commutator length of powers of g. It is known that for n > 2, SL(n,Z) is uniformly perfect; that is, every element is a product of a bounded number of commutators, and hence scl is 0 on all elements. In contrast, most elements in SL(2,Z) have positive scl. This is related to the fact that SL(2,Z) acts naturally on a tree (its Bass-Serre tree) and hence has lots of nontrivial quasimorphisms. In this talk, I will discuss a result on the stable commutator lengths in right-angled Artin groups. This is a broad family of groups that includes free and free abelian groups. These groups are appealing to work with because of their geometry; in particular, each right-angled Artin group admits a natural action on a CAT(0) cube complex. Our main result is an explicit uniform lower bound for scl of any nontrivial element in any right-angled Artin group. This work is joint with Talia Fernos and Max Forester.

Posted January 29, 2016

3:30 pm - 4:20 pm Lockett 277

Roi Docampo Álvarez, Instituto de Ciencias Matemáticas (ICMAT)
The Nash problem for arc spaces

Algebraic varieties (zeros of polynomial equations) often present singularities: points around which the variety fails to be a manifold, and where the usual techniques of calculus encounter difficulties. The problem of understanding singularities can be traced to the very beginning of algebraic geometry, and we now have at our disposal many tools for their study. Among these, one of the most successful is what is known as resolution of singularities, a process that transforms (often in an algorithmic way) any variety into a smooth one, using a sequence of simple modifications.

In the 60's Nash proposed a novel approach to the study of singularities: the arc space. These spaces are natural higher-order analogs of tangent spaces; they parametrize germs of curves mapping into the variety. Just as for tangent spaces, arc spaces are easy to understand in the smooth case, but Nash pointed out that their geometric structure becomes very rich in the presence of singularities.

Roughly speaking, the Nash problem explores the connection between the topology of the arc space and the process of resolution of singularities. The mere existence of such a connection has sparked in recent years a high volume of activity in singularity theory, with connections to many other areas, most notably birational geometry and the minimal model program.

The objective of this talk is to give an overview of the Nash problem. I will give a precise description of the problem, and discuss the most recent developments, including a proof of the Nash conjecture in dimension two, and a partial solution to the Nash problem in arbitrary dimension.

Thursday, February 11, 2016

Posted January 29, 2016

3:30 pm - 4:20 pm Lockett 277

Jiuyi Zhu, LSU
Nodal geometry of Steklov eigenfunctions

The eigenvalue and eigenfunction problem is fundamental and essential in mathematical analysis. The Steklov problem is an eigenvalue problem with its spectral parameter at the boundary of a compact Riemannian manifold. Recently the study of Steklov eigenfunctions has been attracting much attention. We consider the quantitative properties: Doubling inequality and nodal sets. We obtain the sharp doubling inequality for Steklov eigenfunctions on the boundary and interior of manifolds using delicate Carleman estimates. We can ask Yau's type conjecture for the Hausdorff measure of nodal sets of Steklov eigenfunctions on the boundary and interior of the manifold. I will describe some recent progress about this challenging direction. Part of work is joint with C. Sogge and X. Wang.

Monday, February 15, 2016

Posted January 29, 2016

3:30 pm - 4:20 pm Lockett 243

Fang-Ting Tu, National Center for Theoretical Sciences, Taiwan
Modular Forms on Shimura Curves and Hypergeometric Functions

Abstract here

Thursday, February 18, 2016

Posted February 11, 2016

3:30 pm - 4:20 pm Lockett 277

Thomas Parker, Michigan State University
Holomorphic curves, strings, and the GV conjecture

This is a talk on counting solutions of non-linear elliptic PDEs. After presenting the basic idea, I will explain, from two completely different perspectives, how the search for simple examples leads -- rather surprisingly -- to considering holomorphic maps into Calabi-Yau 3-folds X. Such maps are counted by the Gromov-Witten invariants of X, which are an infinite set of rational numbers. In 1998, physicists R. Gopakumar and C. Vafa conjectured that these Gromov-Witten invariants have a hidden structure: they are obtained, by a specific transform, from a set of more fundamental "BPS numbers", which are integers. The talk will conclude with a pictorial proof of the GV conjecture (joint work with E. Ionel) based on the idea of using deformations of almost complex structures to count the contributions of "clusters of curves".

Thursday, March 17, 2016

Posted March 14, 2016

3:30 pm - 4:20 pm Lockett 277

Barbara Rüdiger, Bergische Universität Wuppertal, Germany
Exponential ergodicity of jump-diffusion CIR processes

We analyze exponential ergodicity properties of affine term structure models. For some (Jump -) diffusion CIR processes, in particular the CIR process and the basic affine jump diffusion process (BAJD), we prove Harris recurrence properties. This permits in particular to calibrate the parameters of the model. These results are based on joint articles with V. Mandrekar, Peng Jin, Chiraz Trabelsi, and Jonas Kremer . All models will be introduced in this talk.

Friday, April 29, 2016

Posted April 15, 2016

4:00 pm - 4:50 pm Lockett 277

Structure of Entropy soutions of Hyperbolic conservation laws in space dimension

Hyperbolic Conservation laws in one space dimension has been studied for quite a long time starting from Lax and Oleinik.Main questions related to the existence of numbers shocks and nature of the solutions was not well understood. In this talk I will discuss these questions when the flux is convex.

Thursday, September 22, 2016

Posted September 7, 2016

3:30 pm - 4:20 pm Lockett 9

Karl Mahlburg, Department of Mathematics, LSU
Classical partition identities and automorphic forms

I will discuss my work on the deep connections between automorphic forms and partition identities. These include classical results such as the famous "sum-product" identities of Euler, Rogers-Ramanujan, Andrews-Gordon, and Schur, as well as more recent identities arising from affine Lie algebras and Lepowsky-Wilson's program of vertex operator algebras; a prominent example is due to Capparelli. Although these identities are of interest due to their intrinsic combinatorics and algebraic applications, they also often display automorphic properties, with examples of theta functions, modular functions, mock modular forms, and false theta functions. Some of these connections were only discovered recently, and have led to applications including asymptotic formulas, algebraicity, congruences, and probabilistic interpretations.

Thursday, December 1, 2016

Posted October 25, 2016

3:30 pm - 4:20 pm Lockett 9

Christof Geiss, UNAM Mexico
Geometric construction of semisimple Lie algebras - the non simply laced cases.

Abstract: After an unpublished manuscript by Schofield it is nowadays folklore
how to construct the universal enveloping algebra U(n) of the positive part
n of a symmetric Kac-Moody Lie algebra in terms of constructible functions
on the complex representation spaces of a quiver of the corresponding type.
This fails in the non-symmetric cases because the corresponding weighted quivers
can not be realized over an algebraically closed field.

In joint work with B. Leclerc and J. Schroeer we remedy this situation partially
by considering constructible functions on the representations of projective
dimension on certain 1-Iwanaga-Gorenstein algebras. However, for now this
approach works only in the Dynkin cases since we need to construct explicitly
for each root vector a non-vanishing constructible function.

Friday, January 20, 2017

Posted January 13, 2017

3:30 pm - 4:20 pm Lockett 277

Priyam Patel, UC Santa Barbara, Department of Mathematics
Quantitative methods in hyperbolic geometry

Abstract: Peter Scott's famous result states that the fundamental groups of hyperbolic surfaces are subgroup separable, which has many powerful consequences. For example, given any closed curve on such a surface, potentially with many self-intersections, there is always a finite cover to which the curve lifts to an embedding. It was shown recently that hyperbolic 3-manifold groups share this separability property, and this was a key tool in Ian Agol's resolution to the Virtual Haken and Virtual Fibering conjectures for hyperbolic 3-manifolds.
I will begin this talk by giving some background on separability properties of groups, hyperbolic manifolds, and these two conjectures. There are also a number of interesting quantitative questions that naturally arise in the context of these topics. These questions fit into a recent trend in low-dimensional topology aimed at providing concrete topological and geometric information about hyperbolic manifolds that often cannot be gathered from existence results alone. I will highlight a few of them before focusing on a quantitative question regarding the process of lifting curves on surfaces to embeddings in finite covers.

Monday, January 23, 2017

Posted January 15, 2017

3:30 pm - 4:20 pm Lockett 277

Vu Hoang, Rice University, Department of Mathematics
Singularity formation for equations of fluid dynamics

The basic equations of fluid mechanics were written down about 200 years
ago by Euler. To this day, they present a challenge for mathematical analysis and
many basic questions are still unsolved. One of these basic concerns the issue
of finite-time singularity formation versus global regularity. A great obstacle
for mathematical analysis is the fact that these equations involve both nonlinear
and non-local interactions. In my talk, I will describe recent efforts to understand the
mechanisms that are behind the singularity formation in fluid equations, starting from simple
model equations.

Wednesday, January 25, 2017

Posted January 16, 2017

3:30 pm - 4:20 pm Lockett 277

Aynur Bulut, Princeton University, Department of Mathematics
Recent developments on deterministic and probabilistic well-posedness for nonlinear Schrödinger and wave equations.

Abstract: Dispersive equations such as nonlinear Schrödinger and wave equations arise as mathematical models in a variety of physical settings, including models of plasma physics, the propagation of laser beams, water waves, and the study of many-body quantum mechanics. They also serve as model equations for studying fundamental issues in many aspects of nonlinear partial differential equations. Key questions in the analysis of these equations include issues of well-posedness (for instance, existence of solutions, uniqueness of these solutions, and their continuous dependence on initial data in appropriate topologies) locally in time, long-time existence and behavior of solutions, and, conversely, the possible existence of solutions which blow-up in finite time.
In this talk, we will give an overview of several recent results concerning the local and global (long-time) theory, including some results where probabilistic tools are used to obtain estimates for randomly chosen initial data which are not available in deterministic settings. A recurring theme (and oftentimes obstacle) is the notion of supercriticality arising from the natural scaling of the equation - seeking to characterize long-time behavior of solutions when the relevant scale-invariant norms are not controlled by the conserved energy, or for initial data of very low regularity. The techniques involved include input from several areas of mathematics, including ideas arising in many areas of PDE, harmonic analysis, and probability.

Friday, January 27, 2017

Posted January 16, 2017

3:30 pm - 4:20 pm Lockett 277

Marcel Bischoff, Vanderbilt
Subfactors, Fusion Categories and Conformal Nets

Abstract: Von Neumann algebras were mainly introduced to understand quantum theory and group representations. A factor is a von Neumann algebra with trivial center and an inclusion of two factors is called a subfactor. Finite index subfactors, in some sense, describe quantum symmetries which generalize finite groups. Similarly, fusion categories generalize the representation categories of finite groups. One can use von Neumann algebras to study chiral conformal field theory via so-called conformal nets. It turns out that conformal nets are a natural source of subfactors and fusion categories. It is an exciting open question if all fusion categories and subfactors come from conformal nets. I will introduce these three concepts and their interaction and discuss some recent results on the structure of inclusions of conformal nets and their representation theory.

Monday, January 30, 2017

Posted January 19, 2017

3:30 pm - 4:20 pm tba

Tian Yang, Stanford University
Mapping class group action on character varieties and the ergodicity

Abstract: Character varieties of a surface are central objects in several branches of mathematics, such as low dimensional topology, algebraic geometry, differential geometry and mathematical physics. On the character varieties, there is a tautological action of the mapping class group - the group of symmetries of the surface, which is expected to be ergodic in certain cases. In this talk, I will review related results toward proving the ergodicity and introduce two long standing and related conjectures: Goldman's Conjecture and Bowditch's Conjecture. It is shown by Marche and Wolff that the two conjectures are equivalent for closed surfaces. For punctured surfaces, we disprove Bowditch's Conjecture by giving counterexamples, yet prove that Goldman's Conjecture is still true in this case.

Friday, February 3, 2017

Posted January 15, 2017

3:30 pm - 4:20 pm

Cheng Yu, UT Austin
Weak solutions to the compressible Navier-Stokes equations

In this talk, we will discuss the construction of weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation. The main contribution is to derive the Mellet-Vasseur type inequality for the weak solutions, even if it is not verified by the first level of approximation. This provides existence of global solutions for the compressible Navier-Stokes equations with large data. This is a joint work with A. Vasseur.

Monday, February 6, 2017

Posted January 30, 2017

3:30 pm - 4:20 pm Lockett 277

Anton Zeitlin, Columbia University
Generalized Teichmüller Spaces, Spin Structures and Ptolemy Transformations

Abstract: Teichmüller space, which parameterizes surfaces, is a fundamental space that is important in many areas of mathematics and physics. In recent times generalizations of this space have been intensely studied. The examples of such higher Teichmüller spaces are given by the so-called super-Teichmüller spaces.
These appear as a natural object when studying a combinatorial approach to spin structures on Riemann surfaces and the generalization to supermanifolds. Super means that the structure sheaf is Z/2Z graded and contains odd or anti-commuting coordinates. The super-Teichmüller spaces are higher Teichmüller spaces corresponding to supergroups, which play an important role in geometric topology, algebraic geometry and mathematical physics. There the anti-commuting variables correspond to Fermions. After the introduction of these spaces, I will provide the solution of a long-standing problem of describing the analogue of Penner coordinates on super-Teichmüller space and its generalizations. The importance of these coordinates is justified by two remarkable properties: the action of the mapping class group, expressed via the so-called Ptolemy transformations, is rational, and the Weil-Petersson form is given by a simple explicit formula. I will end outlining some of the many emerging applications of this theory.

Thursday, February 16, 2017

Posted October 11, 2016

3:30 pm - 4:20 pm Lockett 277

Christopher Sogge, Johns Hopkins University J. J. Sylvester Professor of Mathematics
On the concentration of eigenfunctions

I shall present some results in global harmonic analysis that concern properties of eigenfunctions on compact Riemannian manifolds. Using local arguments we can show that $L^p$ norms of eigenfunctions over the entire manifold are saturated if and only if there are small balls (if $p$ is large) or small tubular neighborhoods of geodesics (if $p$ is small) on which the eigenfunctions have very large $L^p$ mass. Neither can occur on manifolds of nonpositive curvature, or, more generally, on manifolds without conjugate points.

Thursday, February 23, 2017

Posted January 31, 2017

3:30 pm - 4:20 pm Locket 277

Barbara Rüdiger, Bergische Universität Wuppertal - Germany
The Enskog process and its relation to the Boltzmann equation

Abstract: The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under suitable hypotheses. The distribution of any solution to the system at each fixed time is shown to be unique when the density exists. The existence of a probability density for the time-marginals of the velocity is verified in the case where the initial condition is Gaussian, and is shown to be the density of an invariant measure. This is a joint work with S. Albeverio and P. Sundar.

Thursday, March 30, 2017

Posted October 25, 2016

3:30 pm - 4:20 pm Lockett 277

Qing Xiang, University of Delaware
Applications of Linear Algebraic Methods in Combinatorics and Finite Geometry

Abstract: Most combinatorial objects can be described by incidence, adjacency, or some other (0,1)-matrices. So one basic approach in combinatorics is to investigate combinatorial objects by using linear algebraic parameters (ranks over various fields, spectrum, Smith normal forms, etc.) of their corresponding matrices. In this talk, we will look at some successful examples of this approach; some examples are old, and some are new. In particular, we will talk about the recent bounds on the size of partial spreads of H(2d-1,q^2) and on the size of partial ovoids of the Ree-Tits octagon.

Thursday, April 6, 2017

Posted March 7, 2017

3:30 pm - 4:20 pm Lockett 277

Peter Jorgensen, Newcastle University
SL_2-tilings, infinite triangulations, and continuous cluster categories

Abstract: An SL_2-tiling is an infinite grid of positive integers such that each adjacent 2x2-submatrix has determinant 1. These tilings were introduced by Assem, Reutenauer, and Smith for combinatorial purposes. We will show that each SL_2-tiling can be obtained by a procedure called Conway--Coxeter counting from certain infinite triangulations of the circle with four accumulation points. We will see how properties of the tilings are reflected in the triangulations. For instance, the entry 1 of a tiling always gives an arc of the corresponding triangulation, and 1 can occur infinitely often in a tiling. On the other hand, if a tiling has no entry equal to 1, then the minimal entry of the tiling is unique, and the minimal entry can be seen as a more complex pattern in the triangulation. The infinite triangulations also give rise to cluster tilting subcategories in a certain cluster category with infinite clusters related to the continuous cluster categories of Igusa and Todorov. The SL_2-tilings can be viewed as the corresponding cluster characters. This is a report on joint work with Christine Bessenrodt and Thorsten Holm.

Thursday, September 14, 2017

Posted August 24, 2017

3:30 pm - 4:20 pm Lockett 277

Shea Vela-Vick, Louisiana State University
Contact geometry and Heegaard Floer theory

Abstract: Among the most transformative applications of Ozsvath and Szabo's Heegaard Floer theory is to the study of contact structures on 3-manifolds. Ozsvath and Szabo first identified an invariant of contact structures taking values in their Heegaard Floer homology in 2002. Since its definition, this invariant has been responsible for a tremendous amount of progress in our understanding of tight contact structures. A steady stream of evidence suggests subtle links between geometric characteristics of contact structures and the algebraic formalism present in Heegaard Floer theory. In this talk, we will discuss how the flow of ideas between contact geometry and Floer theory can be leveraged to establish significant results in each context.

Thursday, September 21, 2017

Posted August 22, 2017

3:30 pm - 4:20 pm

Hongyu He, Department of Mathematics, LSU
Branching Laws and Interlacing Relation

Abstract: Let $H$ be a subgroup of a compact group $G$. Then any irreducible unitary representation of $G$, when restricted to $H$, decomposes into a direct sum of irreducible representations of $H$. A description of such a decomposition is often called a branching law. They are important in harmonic analysis, quantum mechanics and number theory. In this talk, I shall discuss the branching laws of the discrete series of the noncompact unitary groups and the recent progress towards the local Gan-Gross-Prasad conjectures. Discrete series representations were classified by Harish-Chandra in the sixties and played a fundamental role in Langland's program.

Thursday, September 28, 2017

Posted August 25, 2017

3:30 pm - 4:20 pm Lockett 277

John Etnyre, Georgia Institute of Technology
Curvature and contact topology

Abstract: Contact geometry is a beautiful subject that has important interactions with topology in dimension three. In this talk I will give a brief introduction to contact geometry and discuss its interactions with Riemannian geometry. In particular I will discuss a contact geometry analog of the famous sphere theorem and more generally indicate how the curvature of a Riemannian metric can influence properties of a contact structure adapted to it. This is joint work with Rafal Komendarczyk and Patrick Massot.

Thursday, November 16, 2017

Posted September 1, 2017

3:30 pm - 4:20 pm Lockett 277

Yifan Yang, National Taiwan University
Some evaluations of hypergeometric functions from theory of Shimura curves

Abstract: Shimura curves are generalizations of classical modular curves. Because of the lack of cusps on Shimura curves, most of the methods for classical modular curves cannot possibly be extended to the case of Shimura curves. However, in recent years, there have been some methods for Shimura curves emerging in literature. Among them, one method is to realize modular forms in terms of solutions of the so-called Schwarzian differential equations. In the case where a Shimura curve has genus 0 and exactly three elliptic points, this means that modular forms can be expressed in terms of hypergeometric functions. In this talk, we will explain how this idea, together with arithmetic properties and CM theory of Shimura curves, leads to some beautiful evaluations of hypergeometric functions.

Thursday, January 11, 2018

Posted December 17, 2017

3:30 pm - 4:20 pm Lockett 277

Susanna Dann, Technical University of Vienna
Bounding marginal densities via affine isoperimetry

Abstract: Let $\mu$ be a probability measure on $R^n$ with a bounded density $f$. We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there is a trade-off between the strength of such bounds and the probability with which they hold. Our proof rests on new affinely-invariant extremal inequalities for certain averages of $f$ on the Grassmannian and affine Grassmannian. These are motivated by Lutwak's dual affine quermassintegrals for convex sets. We show that key invariance properties of the latter, due to Grinberg, extend to families of functions. The inequalities we obtain can be viewed as functional analogues of results due to Busemann--Straus, Grinberg and Schneider. As an application, we show that without any additional assumptions on $\mu$, any marginal $\pi_E(\mu)$, or a small perturbation thereof, satisfies a nearly optimal small-ball probability.

Friday, January 19, 2018

Posted January 12, 2018

3:30 pm - 4:20 pm Lockett 241

Jake Fillman, Virginia Tech
Spectral properties of quasicrystals

Abstract: Discovered in the early 1980s by Dan Shechtman, quasicrystals are solids that simultaneously exhibit aperiodicity (a lack of translation symmetries) and long-range order (quantified by the presence of Bragg peaks in their diffraction patterns). We will discuss almost-periodic Schroedinger operators, which supply a rich family of operator-theoretic models of quasicrystals. Our discussion will center around the spectral properties of the underlying operator and transport properties of the associated quantum dynamics. We will discuss how some of our results may be viewed as an inverse spectral theoretic obstruction to solving Deift's conjecture for the KdV equation with current technology. We will conclude with a discussion of results in higher dimensions that are motivated by the Bethe--Sommerfeld conjecture.

Monday, January 22, 2018

Posted January 13, 2018

3:30 pm - 4:20 pm Lockett 241

Galyna Dobrovolska, Columbia University
A geometric Fourier transform, noncommutative resolutions, and Hilbert schemes

Abstract: I will start by defining and computing an example of a geometric Fourier transform for constructible functions, and more generally for constructible sheaves. Next I will explain how geometric representation theory can be used to study categories of modules over Lie algebras and more general algebras which quantize symplectic resolutions. Lastly I will apply the above techniques in the case of the Hilbert scheme of points in the plane. (This talk is based on a joint work in progress with R. Bezrukavnikov and I. Loseu and on my Ph.D. thesis)

Wednesday, January 24, 2018

Posted January 12, 2018

3:30 pm - 4:20 pm Lockett 241

Christine Lee, University of Texas at Austin
Understanding quantum link invariants via surfaces in 3-manifolds

Abstract: Quantum link invariants lie at the intersection of hyperbolic geometry, 3-dimensional manifolds, quantum physics, and representation theory, where a central goal is to understand its connection to other invariants of links and 3-manifolds. In this talk, we will introduce the colored Jones polynomial, an important example of quantum link invariants. We will discuss how studying properly embedded surfaces in a 3-manifold provides insight into the topological and geometric content of the polynomial. In particular, we will describe how relating the definition of the polynomial to surfaces in the complement of a link shows that it determines boundary slopes and bounds the hyperbolic volume of many links, and we will explore the implication of this approach on these classical invariants.

Friday, January 26, 2018

Posted January 19, 2018

3:30 pm - 4:20 pm Lockett 241

Shawn X. Cui, Stanford, Institute for Theoretical Physics
Four Dimensional Topological Quantum Field Theories

Abstract: We give an introduction to topological quantum field theories (TQFTs), which have wide applications in low dimensional topology, representation theory, and topological quantum computing. In particular, TQFTs provide invariants of smooth manifolds. We give an explicit construction of a family of four dimensional TQFTs. The input to the construction is a class of tensor categories called $G$-crossed braided fusion categories where $G$ is any finite group. We show that our TQFTs generalize most known examples such as Yetter's TQFT and the Crane-Yetter TQFT. It remains to check if the resulting invariant of 4-manifolds is sensitive to smooth structures. It is expected that the most general four dimensional TQFTs should arise from spherical fusion 2-categories, the proper definition of which has not been universally agreed upon. Indeed, we prove that a $G$-crossed braided fusion category corresponds to a 2-category which does not satisfy the criteria to be a spherical fusion 2-category as defined by Mackaay. Thus the question of what axioms properly define a spherical fusion 2-category is open.

Wednesday, January 31, 2018

Posted January 22, 2018

3:30 pm - 4:20 pm Lockett 241

Larry Rolen, Trinity College Dublin & Georgia Tech
Jensen-Polya Criterion for the Riemann Hypothesis and Related Problems

Abstract: In this talk, I will summarize forthcoming work with Griffin, Ono, and Zagier. In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann's Xi-function. This hyperbolicity has been proved for degrees d <= 3. We obtain an arbitrary precision asymptotic formula for the derivatives $Xi^{(2n)}(0)$, which allows us to prove the hyperbolicity of 100 % of the Jensen polynomials of each degree. We obtain a general theorem which models such polynomials by Hermite polynomials. In the case of Riemann's Xi-function, this proves the GUE random matrix model prediction for the distribution of zeros in derivative aspect. This general condition also confirms a conjecture of Chen, Jia, and Wang on the partition function.

Friday, February 2, 2018

Posted January 21, 2018

3:30 pm - 4:20 pm Lockett 241

Chun-Hung Liu, Princeton University
Graph minors and topological minors

Abstract: Minors and topological minors are two closely related graph containment relations that have attracted extensive attentions in graph theory. Though giant breakthroughs have been made over decades, several questions about these two relations remain open, especially for topological minors. This talk addresses part of our recent work in this direction, including a proof of Robertson's conjecture about well-quasi-ordering graphs by the topological minor relation, a complete characterization of the graphs having the Erdos-Posa property with respect to topological minors which answers a question of Robertson and Seymour, and a proof of Thomas' conjecture on half-integral packing. More open questions, such as Hadwiger's conjecture on graph coloring and its variations and relaxations, will be discussed in this talk.

Monday, February 5, 2018

Posted January 30, 2018

3:30 pm - 4:20 pm Lockett 241

Andrew Zimmer, William and Mary
Non-positive curvature in several complex variables

Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, sometimes this metric satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity) and one can then use these conditions to understand holomorphic maps.

Tuesday, March 6, 2018

Posted February 22, 2018

3:30 pm - 4:20 pm Lockett 284

Wen-Ching Winnie Li, Pennsylvania State University
Distribution of primes

Abstract: The distribution of prime numbers has been one of the central topics in number theory. It has a deep connection with the zeros of the Riemann zeta function. The concept of "primes" also arises in other context. For example, in a compact Riemann surface, as introduced by Selberg, primitive closed geodesic cycles play the role of primes; while in a finite quotient of a finite-dimensional building, for each positive dimension, there are primes of similar nature. In this talk we shall discuss the distributions of such primes and their connections with the analytic behavior of the associated zeta and L-functions.

Thursday, March 22, 2018

Posted December 17, 2017

3:00 pm - 3:50 pm Lockett 277

Guozhen Lu, University of Connecticut
Harmonic analysis on hyperbolic spaces and Sharp geometric inequalities

Abstract: Sharp geometric and functional inequalities play an important role in modern analysis, geometry and partial differential equations. We will begin the talk with some overall review on the best constants and maximizers (aka optimizers) for geometric inequalities such as Sobolev inequalities, Hardy-Trudinger-Moser inequalities, and Caffarelli-Kohn-Nirenberg inequalities, etc. Then we will briefly explain why such inequalities are useful in analysis and geometry. We will then review the Poincare model of hyperbolic spaces. Next, we will describe some recent works using the techniques of harmonic analysis on hyperbolic spaces to establish optimal geometric inequalities. These include the sharp Hardy-Adams inequalities on hyperbolic balls and Hardy-Sobolev-Mazya inequalities on upper half spaces or hyperbolic balls. Using the Fourier analysis on hyperbolic spaces, we will be able to establish sharper inequalities than those known classical inequalities in the literature. This talk in intended for general audience including graduate students.

Thursday, April 12, 2018

Posted December 26, 2017

3:30 pm - 4:20 pm Lockett 277

Stefan Kolb, Newcastle University
Quantum symmetric pairs

Abstract: Since they arose in the 1980s, quantum groups have become an integral part of representation theory with many deep applications, including canonical bases, link invariants and quantum integrable systems. Quantum symmetric pairs were originally invented to perform quantum group analogs of harmonic analysis on symmetric spaces. Over the past five years it has become increasingly clear that many of the applications and constructions for quantum groups allow analogs for quantum symmetric pairs. In this talk I will give an introduction to the theory of quantum symmetric pairs and explain some of the recent developments, illustrating them, where possible, in the simplest example of quantum sl(2).

Thursday, April 19, 2018

Posted January 12, 2018

3:30 pm - 4:20 pm Lockett 277

Birge Huisgen-Zimmermann, University of California, Santa Barbara
Representations of Quivers with Relations

Abstract: It is well known that the representations of a finite dimensional algebra may be viewed as representations of a certain quiver (insider jargon for a finite directed graph). We will start by outlining the ultimate goals pursued in the theory of such representations and illustrate them with classical results and examples. In particular, we will discuss and exemplify the notions of tame and wild representation type.

Then we will zero in on a geometric approach to classifying representations of a quiver. A priori, "degenerations" of a given representation appear to constitute an obstacle on the road to classification. We will explain how this negative can be turned into a positive by harnessing degeneration theory towards the classification goal.

Thursday, April 26, 2018

Posted January 30, 2018

3:30 pm - 4:20 pm Lockett 277

Luis Silvestre, University of Chicago
Integro-differential equations

Abstract: Integro-differential equations have been a very active area of research in recent years. In this talk we will explain what they are and in what sense they are similar to more classical elliptic partial differential equations. We will discuss connections with problems in probability, fluids and statistical mechanics.

Wednesday, October 3, 2018

Posted September 26, 2018

3:30 pm - 4:20 pm Lockett 232

Alexey Karapetyants, Southern Federal University, Russia and SUNY Albany
On Bergman type spaces of functions of nonstandard growth and related questions.

We study various Banach spaces of holomorphic functions on the unit disc and half plane. As a main question we investigate the boundedness of the corresponding holomorphic projection. We exploit the idea of V.P.Zaharyuta, V.I.Yudovich (1962) where the boundedness of the Bergman projection in Lebesgue spaces was proved using Calderon-Zygmund operators. We treat the cases of variable exponent Lebesgue space, Orlicz space, Grand Lebesgue space and variable exponent generalized Morrey space. The major idea is to show that the approach can be applied to a wide range of function spaces. This opens a door in a sense for introducing and studying new function spaces of Bergman type in complex analysis. We also study the rate of growth of functions near the boundary in spaces under consideration and their approximation by mollifying dilations.

Thursday, October 11, 2018

Posted August 29, 2018

3:30 pm - 4:20 pm Lockett 232

Guillermo Goldsztein , School of Mathematics, Georgia Institute of Technology
Synchronization of pendula clocks and metronomes

Abstract: In 1665, Huygens discovered that, when two pendulum clocks
hanged from a same wooden beam supported by two chairs, they synchronize
in anti-phase mode. Metronomes provides a second example of oscillators
that synchronize. As it can be seen in many YouTube videos, metronomes
synchronize in-phase when oscillating on top of the same movable surface.
In this talk, we will review these phenomena, introduce a mathematical
model, and analyze the the different physical effects. We show that, in a
certain parameter regime, the increase of the amplitude of the
oscillations leads to a bifurcation from the anti-phase synchronization
being stable to the in-phase synchronization being stable. We argue that
this may explain the experimental observations.

Thursday, October 25, 2018

Posted August 14, 2018

3:30 pm - 4:20 pm Lockett 232

Hongjie Dong, Brown University
Interior and boundary regularity for the incompressible Navier-Stokes Equations

Abstract: The regularity theory for fluid equations is at the heart of fluid flow modeling and leads to many new ideas in scientific computing, differential equations, and statistics, and has been characterized as one of the outstanding technical challenges in this era. For sufficiently regular data, the local strong solvability of the incompressible Navier-Stokes equations is well understood. Such solution is unique and locally smooth in both spatial and time variables. On the other hand, the global in time strong solvability is an outstanding open problem for d geq 3. Another important type of solutions are called Leray-Hopf weak solutions. In the pioneering works of Leray and Hopf, it is shown that evolving from any divergence-free vector field in $L_2$, there exists at least one Leray-Hopf weak solution to the Navier-Stokes Equations. Although the problems of uniqueness and regularity of Leray-Hopf weak solutions are still open, solutions are known to be partially regular in certain cases, and fully regular under certain criteria. In this talk, I will first review some previous results on the conditional regularity of solutions to the incompressible Navier-Stokes equations in the critical Lebesgue spaces, and then discuss a recent work which mainly addressed the boundary regularity issue.

Thursday, November 8, 2018

Posted October 11, 2018

3:30 pm - 4:20 pm Lockett 232

Scott Ahlgren, University of Illinois at Urbana-Champaign
Kloosterman sums, Maass cusp forms, and partitions.

Abstract: Kloosterman sums are exponential sums which appear naturally in a wide range of applications in number theory. Maass cusp forms are real-analytic automorphic forms which are eigenfunctions of the Laplace operator; they encode information about a variety of arithmetical problems. The partition function is the basic function of additive number theory: it counts the number of ways to break a natural number into parts. I will describe these objects and their history, discuss connections between them, and discuss some deep conjectures about their properties. I will also describe some recent applications to the theory of partitions.

Thursday, November 29, 2018

Posted September 5, 2018

3:30 pm - 4:20 pm Lockett 232

Ko Honda, UCLA
Convex hypersurface theory in higher-dimensional contact topology

Abstract: Contact 3-manifolds occupy a central role in low-dimensional topology due to their interactions with Floer-theoretic invariants. Convex surface theory and bypasses are extremely powerful tools for analyzing contact 3-manifolds and in particular have been successfully applied to many classification problems. After reviewing convex surface theory in dimension three, we explain how to generalize many of their properties to higher dimensions. This is joint work with Yang Huang.

Friday, January 11, 2019

Posted December 4, 2018

3:30 pm - 4:30 pm Lockett 232

Ruoyu Wu, University of Michigan
Weakly interacting particle systems on random graphs: from dense to sparse

Abstract: We consider the asymptotic behaviors of weakly interacting (mean-field) particle systems on random graphs that could be dense or sparse. The system consists of a large number of nodes in which the state of each node is governed by a stochastic process that has a mean-field type interaction with the neighboring nodes. Such systems arise in many areas, including but not limited to neuroscience, queueing theory and social sciences, which we will discuss in this talk.

In the dense graph case, the limiting system is described by the classic McKean--Vlasov equation. Law of large numbers, propagation of chaos, and central limit theorems are established and turn out to be the same as those in the complete graph case.

In the sparse case, the limiting system is quite different and depends heavily on the graph structure. We obtain an autonomous characterization of the local dynamics of a typical node and its neighbors when the limiting graph is a D- regular tree or a Galton--Watson tree.

If time permits, certain queueing systems with non-mean-field interactions will be discussed.

Wednesday, January 23, 2019

Posted January 11, 2019

3:30 pm - 4:30 pm Lockett 232

William Feldman, University of Chicago
Interfaces in inhomogeneous media: pinning, hysteresis, and facets

Abstract: I will discuss some models for the shape of liquid droplets on rough solid surfaces. The framework of homogenization theory allows to study the large scale effects of small scale surface roughness, including interesting physical phenomena such as contact line pinning, hysteresis, and formation of facets.

Friday, January 25, 2019

Posted January 22, 2019

3:30 pm - 4:20 pm Lockett 232

Wenqing Hu, Missouri University of Science and Technology
Stochastic Approximations, Diffusion Limit and Randomly Perturbed Dynamical Systems - a probabilistic approach to machine learning

Abstract: The remarkable empirical performance of the Stochastic Gradient Descent (SGD) algorithm with constant learning rate has led to the effective training of many large-scale machine learning models in modern data science.

In this talk, we provide a theoretical understanding of the effectiveness of the SGD algorithm from a probabilistic approach. As the learning rate tends to zero, a stochastic differential equation is introduced to describe the diffusion limit of the discrete recursive scheme used in SGD. Based on this diffusion limit, we connect SGD with a randomly perturbed gradient system. This connection enables us to understand the stochastic dynamics of SGD via delicate probabilistic techniques in stochastic analysis (stochastic calculus). As examples, we will discuss several important theoretical problems around SGD that are raised by the daily practice of data scientists: How does SGD escape from stationary points (including saddle points and local minima)? Does SGD finally choose a local minimum point that agrees with the global minimum point of the loss function? How does SGD's noise covariance structure implicitly affect the regularization properties of its solution path? Our probabilistic approach provides insights into these problems through a unified mathematical framework that can also be carried to many other stochastic approximation algorithms.

Thursday, January 31, 2019

Posted January 26, 2019

3:30 pm - 4:20 pm Lockett 232

Huanchen Bao, University of Maryland
From Schur-Weyl duality to quantum symmetric pairs

Abstract: The classical Schur-Weyl duality relates the representation theory of general linear Lie algebras and symmetric groups. Drinfeld and Jimbo independently introduced quantum groups in their study of exactly solvable models, which leads to a quantization of the Schur duality relating quantum groups of general linear Lie algebras and Hecke algebras of symmetric groups.

In this talk, I will explain the generalization of the (quantized) Schur-Weyl duality to other classical types. This new duality leads to a theory of canonical bases arising from quantum symmetric pairs generalizing Lusztig''s canonical bases on quantum groups.

Monday, February 4, 2019

Posted January 28, 2019

3:30 pm - 4:20 pm Lockett 232

Andrei Tarfulea, University of Chicago
Existence, continuation, and lower mass bounds for the Landau equation.

Abstract: Kinetic equations model gas and particle dynamics, specifically focusing on the interactions between the micro-, meso-, and macroscopic scales. Mathematically, they demonstrate a rich variety of nonlinear phenomena, such as hypoellipticity through velocity-averaging and Landau damping. The question of well-posedness remains an active area of research.
In this talk, we look at the Landau equation, a mathematical model for plasma physics arising from the Boltzmann equation as so-called grazing collisions dominate. Previous results are in the perturbative regime, or in the homogeneous setting, or rely on strong a priori control of the solution (the most crucial assumption being a lower bound on the density, as this prevents the elliptic terms from becoming degenerate).
We prove that the Landau equation has local-in-time solutions with no additional a priori assumptions; the initial data is even allowed to contain regions of vacuum. We then prove a "mass spreading" result via a probabilistic approach. This is the first proof that a density lower bound is generated dynamically from collisions. From the lower bound, it follows that the local solution is smooth, and we establish the mildest (to date) continuation criteria for the solution to exist for all time.

Thursday, February 7, 2019

Posted November 21, 2018

3:30 pm - 4:20 pm Lockett 232

Daniel Nakano, University of Georgia
On Donkin's Conjectures

Abstract: Let $G$ be a simple, simply connected algebraic group over an algebraically closed field of prime characteristic. Recent work of Kildetoft and Nakano and of Sobaje has shown close connections between two long-standing conjectures of Donkin: one on tilting modules and the lifting of projective modules for Frobenius kernels of $G$ and another on the existence of certain filtrations of $G$-modules. In this talk, I will survey recent results in this area and present new results where we verify the one direction of Donkin's $(p,r)$ Filtration Conjecture for rank 2 groups for all primes. I will also show a recently discovered counterexample to the Tilting Module Conjecture. These results represent joint work with Christopher Bendel, Cornelius Pillen and Paul Sobaje.

Thursday, February 14, 2019

Posted August 29, 2018

3:30 pm - 4:20 pm Lockett 232

Iván Angiono, Universidad Nacional de Cordoba (National University of Cordoba)
Finite-dimensional pointed Hopf algebras over abelian groups

Abstract: Hopf algebras appeared in the 50s associated to algebras of functions of algebraic groups, with a well-known bijection when we restrict to commutative Hopf algebras over the complex numbers. Other classical examples of Hopf algebras are the enveloping algebras of Lie algebras, which in turn are co-commutative. In the 80s Drinfeld and Jimbo introduced quantized versions of these enveloping algebras, which are examples of non-commutative nor co-cocommutative Hopf algebras with several applications to Mathematics and Physics. Related with them, Lusztig introduced in the 90s finite-dimensional versions, the so-called small quantum groups. All these Hopf algebras are pointed: the coradical is a group algebra, which dominates the structure of the Hopf algebra and becomes a first invariant to describe it. In this talk we present the classification of finite-dimensional Hopf algebras whose group is abelian. We start from the basic definitions with the first known examples. Then we recall the Lifting Method introduced by Andruskiewtisch and Schneider, a fundamental step for their classification result when the order of the group is coprime with 210. We describe Nichols algebras of diagonal type (some kind of algebras closely related to our problem) and the classification obtained by Heckenberger. Next we give a presentation by generators and relations and the first consequences of this result. Finally we give a generalization of the Lifting Method to obtain deformations of graded Hopf algebras and the end of the classification, a result by myself, Andruskiewitsch and Garcia Iglesias, and some consequences about tensor categories attached to these Hopf algebras.

Thursday, February 21, 2019

Posted August 22, 2018

3:30 pm - 4:20 pm Lockett 232

Nicolas Andruskiewitsch, Universidad Nacional de Cordoba (National University of Cordoba)
On the classification of finite-dimensional Hopf algebras

Abstract: A gentle overview of the status of the classification of finite-dimensional Hopf algebras with emphasis on the relations with Lie theory.

Thursday, February 28, 2019

Posted October 18, 2018

3:30 pm - 4:20 pm Lockett 232

Matthew Hedden, Michigan State University
Knot theory and algebraic curves

Abstract: The modern study of knots and links has important roots in the theory of algebraic curves, where links encode subtle features of singularities. This thread was taken in interesting new directions in the 20th century, and the interaction between links in 3-dimensional manifolds and algebraic curves in complex surfaces continues to be a rich and beautiful area. In this talk I will survey the subject, from its seeds in the work of Newton to interesting advances which have occurred in the past decade.

Thursday, March 21, 2019

Posted January 9, 2019

3:30 pm - 4:20 pm Lockett 232

Amarjit Budhiraja, UNC Chapel Hill
On Some Calculus of Variations Problems for Rare Event Asymptotics

The theory of large deviations gives decay rates of probabilities of rare events in terms of certain optimal control problems. In general these control problems do not admit simple form solutions and one needs numerical methods in order to obtain useful information. In this talk I will present some large deviation problems where one can use methods of calculus of variations to give explicit solutions to the associated optimal control problems. These solutions then yield explicit asymptotic formulas for probability decay rates in several settings.

Thursday, April 25, 2019

Posted January 17, 2019