LSU
Mathematics

# Calendar

Time interval:   Events:

Monday, August 19, 2019

Posted April 30, 2019

1:00 pm - 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Algebra

This exam is part of the PhD Qualifying Examination in Mathematics. Use this link for the registration form: Comprehensive Exam Registration

Wednesday, August 21, 2019

Posted April 30, 2019

1:00 pm - 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Analysis

This exam is part of the PhD Qualifying Examination in Mathematics. Use this link for the registration form: Comprehensive Exam Registration

Friday, August 23, 2019

Posted April 30, 2019

1:00 pm - 4:00 pm Lockett 232

Comprehensive/PhD Qualifying Exam in Topology

This exam is part of the PhD Qualifying Examination in Mathematics. Use this link for the registration form: Comprehensive Exam Registration

Wednesday, September 4, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Shea Vela-Vick, Louisiana State University
An introduction to low-dimensional topology and contact geometry

Posted August 31, 2019

3:30 pm - 4:30 pm Keisler Lounge, Lockett 321

What We Did This Summer

Monday, September 9, 2019

Posted September 4, 2019

3:30 pm - 4:30 pm Lockett 233

Wei Li, LSU
Fluorescence ultrasound modulated optical tomography (fUMOT) in the radiated transport regime with angularly averaged measurements

We consider an inverse transport problem in fluorescence ultrasound modulated optical tomography (fUMOT) with angularly averaged illuminations and measurements. We study the uniqueness and stability of the reconstruction of the absorption coefficient and the quantum efficiency of the fluorescent probes. Reconstruction algorithms are proposed and numerical validations are performed. This is joint work with Yang Yang and Yimin Zhong, and it is an extension of our previous work done in 2018, where a diffusion model for this problem was considered.

Wednesday, September 11, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Scott Baldridge, Louisiana State University
An introduction to Mirror Symmetry, Calabi-Yau manifolds, and Special Lagrangian Cones

Abstract: In this talk we look at the history of mirror symmetry as it came out of string theory (i.e., a 10-dimensional universe where particles are "strings"). We use that historical account to explain some of the motivation behind studying Calabi-Yau manifolds and special Lagrangian fibrations of these manifolds, which lead to my studying of special Lagrangian cones in my work. The goal is to use this narrative to introduce and discuss common terms (symplectic forms, Lagrangian, fiber bundles and fibrations, etc.) that will be used throughout the graduate student seminar this year. In that sense, this is not going to be an overly technical talk.

Monday, September 16, 2019

Posted September 13, 2019

3:30 pm - 4:30 pm Lockett 233

Isaac Michael, Louisiana State University
Weighted Birman-Hardy-Rellich type Inequalities with Refinements

In 1961, Birman proved a sequence of inequalities valid for functions in C_0^{n}((0, infty)) containing the classical (integral) Hardy inequality and the well-known Rellich inequality. Over the years there has been much effort in improving these inequalities with weights and singular logarithmic refinement terms. Using a simple variable transformation in integrals, we prove a generalization of these inequalities involving unrestricted power-type weights and logarithmic refinement terms, on both the exterior interval (R, infty) and the interior interval (0, R) for any finite R>0. This is based on joint work with Fritz Gesztesy, Lance Littlejohn, and Michael Pang.

Wednesday, September 18, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Justin Murray, Louisiana State University
TBD

Monday, September 23, 2019

Posted September 17, 2019

3:30 pm - 4:30 pm Lockett Hall 237

Farid Bouya, Louisiana State University
Seymour''s Second Neighborhood Conjecture from a Different Perspective

Seymour''s Second Neighborhood Conjecture states that every orientation of every simple graph has at least one vertex $v$ such that the number of vertices of out-distance 2 from $v$ is at least as large as the number of vertices of out-distance 1 from it. We present an alternative statement of the conjecture in the language of linear algebra.

Tuesday, September 24, 2019

Posted August 27, 2019

3:10 pm - 4:00 pm 285 Lockett

Moises Herradon Cueto, Louisiana State University
The local type of difference equations

D-modules allow us to study differential equations through the lens of algebraic geometry. They are widely studied and have been shown to be full of structure. In contrast, the case of difference equations is lacking some of the most basic constructions. We focus on the following question: D-modules have a clear notion of what it means to restrict to a (formal) neighborhood of a point, namely extension of scalars to a power series ring. However, what does it mean to restrict a difference equation to a neighborhood of a point? I will give an answer which encompasses the intuitive notions of a "zero" and a "pole" of a difference equation, but further it is consistent in two more ways. First of all, we can show that restricting a difference equation to a point and to its complement is enough to recover the difference equation. Secondly, there exists a local Mellin transform analogous to the local Fourier transform. The local Fourier transform describes singularities of a D-module on the affine line in terms of the singularities of its Fourier transform. Similarly, the Mellin transform is an equivalence between D-modules on the punctured affine line and difference modules on the line, and we can relate singularities on both sides via this local Mellin transform. I will also talk about how to apply the same ideas to other kinds of difference equations, such as elliptic equations, which generalize difference and differential equations at once.

Wednesday, September 25, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Ryan Leigon, Louisiana State University
TBD

Thursday, September 26, 2019

College of Science Inclusive Excellence Lecture Series

Posted September 5, 2019

3:30 pm - 5:00 pm Hill Memorial Library

Suzanne Lenhart, University of Tennessee
One Health: Connecting Humans, Animals and the Environment

"One Health" is a multidisciplinary approach to improving the health of people, animals and the environment. Environmental, wildlife, domestic animal, and human health fall under the One Health concept. Mathematical models of infectious diseases involving animals, environmental features, and humans will be presented. These models can suggest management policies and predict disease spread, and examples including La Crosse virus and Zika virus will be discussed. (Reception after the talk)

Tuesday, October 1, 2019

Posted September 7, 2019

3:10 pm - 4:00 pm 285 Lockett

Solly Parenti, University of Wisconsin, Madison
Unitary CM Fields and the Colmez Conjecture

In 1993, Pierre Colmez conjectured a formula for the Faltings height of a CM abelian variety in terms of logarithmic derivatives of certain L-functions. I will discuss how we can extend the known cases of the conjecture to a class of unitary CM fields using the recently proven average version of the conjecture.

Posted September 26, 2019

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

1. Winnie Sloan (is an LSU alumna, a Senior Actuarial Assistant for Travelers in St. Paul, MN, and has assisted many of our students who want advice from a professional actuary) is our speaker via skype. 2. Selecting new officers. Pizza will be served.

Wednesday, October 2, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Jiten Ahuja, Louisiana State University
TBD

Monday, October 7, 2019

Posted October 4, 2019

3:30 pm Lockett Hall 237

Zachary Gershkoff, Mathematics Department, LSU
Connectivity in Matroids and Polymatroids

Another way of saying that a matroid is connected is to say that for every pair of elements, there is a U_{1,2}-minor that uses them. We investigate what kind of structure a matroid M has when every two elements of M are in an N-minor for certain N. For 2-polymatroids, we prove a result that''s similar to Brylawski and Seymour''s result that if M is a connected matroid with a connected minor N, and e is in E(M)−E(N), then Me or M/e is connected having N as a minor.

Tuesday, October 8, 2019

Posted September 14, 2019

3:10 pm - 4:00 pm 285 Lockett

Chenliang Huang, Indiana University-Purdue University Indianapolis (IUPUI)
The solutions of gl(m|n) Gaudin Bethe ansatz equation, rational pseudodifferential operators, and the gl(m|n) spaces

We consider the gl(m|n) Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules. Given a solution we describe a reproduction procedure which produces a family of new solutions which we call a population of solutions. We also write a rational pseudodifferential operator invariant under the reproduction procedure. We expect that the coefficients of the expansion of this operator are eigenvalues of the higher Gaudin Hamiltonians acting on the corresponding Bethe vector. The kernels of the numerator and denominator of the rational differential operator consist of rational functions and form a super space. Then we show that the population is canonically identified with the set of complete factorizations of the rational pseudodifferential operator, and with the variety of full super flags in the super space of rational functions. We conjecture that the eigenvectors of the Gaudin Hamiltonians are in a bijection with super spaces of rational functions with the prescribed properties which we call the gl(m|n) spaces.

Wednesday, October 9, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
TBD

Monday, October 14, 2019

Posted September 4, 2019

3:30 pm - 4:30 pm Lockett 233

Phuc Nguyen, Department of Mathematics, Louisiana State University
TBA

Posted October 2, 2019

3:30 pm - 4:30 pm Lockett 233

Phuc Nguyen, Department of Mathematics, Louisiana State University
Weighted and pointwise bounds in measure datum problems with applications

Muckenhoupt-Wheeden type bounds and pointwise bounds by Wolff's potentials are obtained for gradients of solutions to a class of quasilinear elliptic equations with measure data. Such results are obtained globally over sufficiently flat domains in the sense of Reifenberg. The principal operator here is modeled after the $p$-Laplacian, where for the first time a singular case is considered. As an application, sharp existence and removable singularity results are obtained for a class of quasilinear Riccati type equations having a gradient source term with linear or super-linear power growth. This talk is based on joint work with Quoc-Hung Nguyen.

Posted October 11, 2019

3:30 pm Lockett Hall 237

Tara Fife, Louisiana State University
Laminar Matroids and their Generalizations

Abstract: I''ll begin by introducing matroids, nested matroids, and laminar matroids. One characterization of laminar matroids is that for all circuits $C_1cap C_2not=emptyset$, either $C_1$ is in the closure of $C_2$ or $C_2$ is in the closure of $C_1$. We use this characterization to define two infinite families of generalized laminar matroids and give structural results of these classes. This is joint work with James Oxley.

Tuesday, October 15, 2019

Posted October 8, 2019

3:30 pm - 4:30 pm 1034 Digital Media Center

Hongchao Zhang, Louisiana State University
A Nonmonotone Smoothing Newton Algorithm for Weighted Complementarity Problem

Abstract: The weighted complementarity problem, often denoted by WCP, significantly extends the general complementarity problem and can be used for modeling a larger class of problems from science and engineering. In this talk, by introducing a one-parametric class of smoothing functions, we will introduce a smoothing Newton algorithm with nonmonotone line search to solve WCP. We will discuss the global convergence as well as local superlinear or quadratic convergence of this algorithm under assumptions weaker than assuming the nonsingularity of the Jacobian. Some promising numerical results will be also reported.

Posted October 10, 2019

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Abigail Brown, LSU contact for actuary, will come as a guest speaker. She will be discussing interviews, resumes, and other related topics. Pizza will be served.

Wednesday, October 16, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Amit Kumar, Louisiana State University
TBD

Monday, October 21, 2019

Posted October 8, 2019

3:30 pm - 4:30 pm tba

Meeting of Full Professors

Wednesday, October 23, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
TBD

Posted September 11, 2019

3:30 pm - 4:30 pm Lockett 233

Hung Cong Tran, University of Oklahoma
The local-to-global property for Morse quasi-geodesics

Abstract: We show the mapping class group, CAT(0) groups, the fundamental groups of compact 3-manifolds, and certain relatively hyperbolic groups have a local-to-global property for Morse quasi-geodesics. As a consequence, we generalize combination theorems of Gitik for quasiconvex subgroups of hyperbolic groups to the stable subgroups of these groups. In the case of the mapping class group, this gives a combination theorem for convex cocompact subgroups. This is a joint work with Jacob Russell and Davide Spriano.

Thursday, October 24, 2019

Posted October 1, 2019

5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

West Dickens and Alaina Chifici (LSU alumna) from Protective insurance will visit. They will also set up some interviews for Friday October 25 for anyone applying to their internship program. Pizza will be served.

Tuesday, October 29, 2019

Posted August 19, 2019

3:10 pm - 4:00 pm 285 Lockett

Changningphaabi Namoijam, Texas A&M
Transcendence of Hyperderivatives of Logarithms and Quasi-logarithms of Drinfeld Modules

In 2012, Chang and Papanikolas proved the transcendence of certain logarithms and quasi-logarithms of Drinfeld Modules. We extend this result to transcendence of hyperderivatives of these logarithms and quasi-logarithms. To do this, we construct a suitable t-motive and then use Papanikolas' results on transcendence degree of the period matrix of a t-motive and dimension of its Galois group.

Posted September 13, 2019

3:30 pm - 4:20 pm Lockett 232

Marta Lewicka, University of Pittsburgh
Geometry and Elasticity: the Mathematics of Shape Formation

We discuss some mathematical problems combining geometry and analysis, hat arise from the description of elastic objects displaying heterogeneous incompatibilities of strains. These strains may be present in bulk or in thin structures, may be associated with growth, swelling, shrinkage, plasticity, etc. We will describe the effect of such incompatibilities on the singular limits' bidimensional models, in the variational description pertaining to the "non-Euclidean elasticity" and discuss the interaction of nonlinear pdes, geometry and mechanics of materials in the prediction of patterns and shape formation.

Wednesday, October 30, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Nurdin Takenov, Louisiana State University
Braid group and its representation(s)

Abstract: In my presentation I will talk about braid group and its representations. In particular, I will talk about Burau representation and (if there will be enough time) about its generalization.

Posted September 9, 2019

3:30 pm - 4:30 pm Lockett 233

Viet Dung Nguyen, Vietnam Academy of Science and Technology Institute of Mathematics
The higher topological complexity of the complement of fiber type arrangements and related topics

Abstract: In the talk we present our method to compute the higher topological of the complement of fiber type arrangements. The same method will be applied to compute the higher topological complexity for some other spaces.

Thursday, October 31, 2019

Posted October 15, 2019

1:30 pm - 2:30 pm Coates Hall 109

Heuristics for Statistics in Number Theory

Abstract: Last month the sum of three cubes was in the news: mathematicians discovered with a computer how to write 42 as a sum of three cubes and then how to write 3 as a sum of three cubes in a new way; it's in fact expected that both 42 and 3 are a sum of three cubes in infinitely many ways. There are many other patterns in number theory that are expected to occur infinitely often: infinitely many twin primes, infinitely many primes of the form $x^2 + 1$, and so on. The basis for these beliefs is a heuristic way of applying probabilistic ideas to number theory, even though there is nothing probabilistic about perfect cubes or prime numbers. The goal of this talk is to show how such heuristics work and, time permitting, to see a situation where such heuristics break down.

Posted September 13, 2019

3:30 pm - 4:20 pm Lockett 232

Selim Esedoglu , University of Michigan
Algorithms for motion by mean curvature of networks.

Many applications in science and engineering call for simulating the evolution of interfaces (curves in the plane, or surfaces in space), including networks of them, under motion by mean curvature and related geometric flows. These dynamics arise as gradient descent for energies that contain the sum of (sometimes weighted and anisotropic) surface areas of the interfaces in the network. The applications include image processing, computer vision, machine learning, and materials science. There are a plethora of algorithms for simulating motion by mean curvature, especially in the challenging multiphase setting. I will review some of the simplest and most elegant: those that attempt to generate the evolution, including any necessary topological changes, by alternating just a few very efficient operations. They include the threshold dynamics algorithm of Merriman, Bence, and Osher, and the Voronoi implicit interface method of Saye and Sethian. Unfortunately, not all of these extremely streamlined, closely related methods converge to their advertised limit. I will discuss how recent developments in our understanding of some of these algorithms have allowed us to fix their lack of convergence.

Friday, November 1, 2019

Posted October 15, 2019

9:30 am - 10:30 am Allen Hall 123

Applications of Divergence of the Harmonic Series

Abstract: The harmonic series is the sum of all reciprocals $1 + 1/2 + 1/3 + 1/4 + ...$, and a famous counterintuitive result in calculus is that the harmonic series diverges even though its general term tends to 0. This role for the harmonic series is often the only way students see the harmonic series appear in math classes. However, the divergence of the harmonic series turns out to have applications to topics in math besides calculus and to events in your daily experience. By the end of this talk you will see several reasons that the divergence of the harmonic series should be intuitively reasonable.

Monday, November 4, 2019

Posted November 3, 2019

3:30 pm - 4:30 pm Lockett 233

Andrei Tarfulea, Louisiana State University
The Boltzmann equation with slowly decaying initial data

In this talk we look at the Boltzmann equation, a kinetic continuum model for plasma and high-energy gases. We will look at some previous results on well-posedness for the Cauchy problem, before presenting our recent result on local well-posedness (for a much wider range of parameters) with reduced assumptions on the initial data. As an application, our theorem combines with preexisting results to yield a continuation criterion for the larger parameter range. The scope of the talk will be to examine some of the various difficulties and methodologies associated with the Boltzmann collision operator: the physical symmetries, decompositions, and geometric lemmas needed to control (and in some cases extract regularity from) this nonlinear nonlocal interaction.

Tuesday, November 5, 2019

Posted September 9, 2019

3:30 pm - 4:30 pm 1034 Digital Media Center

Jose Garay, Louisiana State University
Localized Orthogonal Decomposition Method with Additive Schwarz for the Solution of Multiscale Elliptic Problems

Abstract: The solution of elliptic Partial Differential Equations (PDEs) with multiscale diffusion coefficients using regular Finite Element methods (FEM) typically requires a very fine mesh to resolve the small scales, which might be unfeasible. The use of generalized finite elements such as in the method of Localized Orthogonal Decomposition (LOD) requires a coarser mesh to obtain an approximation of the solution with similar accuracy. We present a solver for multiscale elliptic PDEs based on a variant of the LOD method. The resulting multiscale linear system is solved by using a two-level additive Schwarz preconditioner. We provide an analysis of the condition number of the preconditioned system as well as the numerical results which validate our theoretical results.

Wednesday, November 6, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Rob Quarles, Louisiana State University
TBD

Posted August 9, 2019

3:30 pm - 4:20 pm Lockett 232

Dejan Slepcev, Carnegie Mellon University
Variational problems on random structures: analysis and applications to data science

Abstract: Modern data-acquisition techniques produce a wealth of data about the world we live in. Extracting the information from the data leads to machine learning/statistics tasks such as clustering, classification, regression, dimensionality reduction, and others. Many of these tasks seek to minimize a functional, defined on the available random sample, which specifies the desired properties of the object sought.

I will present a mathematical framework suitable for studies of asymptotic properties of such, variational, problems posed on random samples and related random geometries (e.g. proximity graphs). In particular we will discuss the passage from discrete variational problems on random samples to their continuum limits. Furthermore we will discuss how tools of applies analysis help shed light on algorithms of machine learning.

Posted September 16, 2019

3:30 pm - 4:30 pm Lockett 233

Jason Behrstock, CUNY Graduate Center and Lehman College
Hierarchically hyperbolic groups: an introduction

Abstract: Hierarchical hyperbolicity provides a uniform framework for working with many important examples, including mapping class groups, right angled Artin groups, Teichmuller space, and others. In this talk I'll provide an introduction to studying groups and spaces from this point of view. This talk will include joint work with M. Hagen and A. Sisto.

Thursday, November 7, 2019

Posted October 21, 2019

3:30 pm - 4:20 pm Lockett 232

Ignacio Nahuel Zurrian, Universidad Nacional de Cordoba (National University of Cordoba)
Bispectrality and commuting operators

Abstract: We will discuss the role of bispectrality in the commuting operators phenomenon. We will also consider situations of different nature, e.g. continuous and discrete variables or a matrix/valued setup. Finally, I would like to explore some very recent results as well as the notion of reflecting operators.

Monday, November 11, 2019

Posted October 5, 2019

3:30 pm - 4:30 pm Lockett Room 233

Matthias Maier, Department of Mathematics Texas A&M University
Simulation of Optical Phenomena on 2D Material Devices

In the terahertz frequency range, the effective (complex-valued) surface conductivity of atomically thick 2D materials such as graphene has a positive imaginary part that is considerably larger than the real part. This feature allows for the propagation of slowly decaying electromagnetic waves, called surface plasmon-polaritons (SPPs), that are confined near the material interface with wavelengths much shorter than the wavelength of the free-space radiation. SPPs are a promising ingredient in the design of novel optical devices, promising "subwavelength optics" beyond the diffraction limit. There is a compelling need for controllable numerical schemes which, placed on firm mathematical grounds, can reliably describe SPPs in a variety of geometries. In this talk we present a number of analytical and computational approaches to simulate SPPs on 2D material interfaces and layered heterostructures. Aspects of the numerical treatment such as absorbing perfectly matched layers, local refinement and a-posteriori error control are discussed. We show analytical results for some prototypical geometries and a homogenization theory for layered heterostructures.

Today, Tuesday, November 12, 2019

Posted November 5, 2019

until 5:30 pm James E. Keisler Lounge (room 321 Lockett)

Actuarial club meeting

Senior, Sarah Davidson, will discuss her internship at CNA Insurance in Chicago

Nick Crifasi from AmeriHealth Caritas in Philadelphia will skype. Nick is an ASA in the Society of Actuaries and is an LSU alumnus.

Nick is requesting that seniors graduating in December or May give him their resume. Seniors graduating in December or May please send your resume to Kevin Li at kli27@lsu.edu, and he will send them to Nick.

Posted October 21, 2019

3:30 pm - 4:20 pm TBD

Nathan Glatt-Holtz, Tulane University
TBD

Tomorrow, Wednesday, November 13, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

Abel Lopez, Louisiana State University
TBD

Thursday, November 14, 2019

Posted September 24, 2019

3:30 pm - 4:20 pm Lockett 232

John Voight, Dartmouth College
Heuristics for units in number rings

Units in number rings are gems of arithmetic, the most famous being the golden ratio and the integer solutions x,y to Pell's equation x^2 - D*y^2 = +/-1 for D > 0. Like gems, they are embedded deeply within. Refined questions about the structure of units remain difficult to answer, for example: how often does it happen that Pell's equation has a solution to the -1 equation? More generally, how often in a number ring is it that all totally positive units are squares? Absent theorems, we may still try to predict the answer to these questions. In this talk, we present heuristics (and some theorems!) for signatures of unit groups inspired by the Cohen-Lenstra heuristics for class groups, but involving an lustrous structure of number rings we call the 2-Selmer signature map. This is joint work with David S. Dummit and Richard Foote and with Ben Breen, Noam Elkies, and Ila Varma.

Monday, November 18, 2019

Posted October 15, 2019

TBA

Steven Leth, University of Northern Colorado
TBA

Posted November 8, 2019

3:30 pm Lockett 233

F. Alberto Gr¨unbaum, University of California, Berkeley
Quantum walks: a nice playground for old and new mathematics.

I will give an ab-initio talk trying to show how some time honored pieces of analysis can be used to answer questions about recurrence of quantum walks. I will start with a quick review of classical random walks and then show how Schur functions (the same I. Schur of many other deep topics) are useful in the quantum case. Recently these Schur functions have been seen to be useful in getting a topological classification of quantum walks that respect certain symmetries but go beyond the translation invariant case. I will not assume any previous knowledge about quantum walks. This is joint work with Jean Bourgain, Luis Velazquez, Reinhard Werner, Albert Werner and Jon Wilkening.

Tuesday, November 19, 2019

Posted October 15, 2019

TBA

Steven Leth, University of Northern Colorado
TBA

Posted October 11, 2019

3:10 pm - 4:00 pm 285 Lockett

Ignacio Nahuel Zurrian, Universidad Nacional de Cordoba (National University of Cordoba)
TBA

Posted September 9, 2019

3:30 pm - 4:30 pm 1034 Digital Media Center

Yakui Huang, Hebei University of Technology
On the Asymptotic Convergence and Acceleration of Gradient Methods

Abstract: We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate the family of gradient methods, we further exploit spectral properties of stepsizes to break the zigzagging pattern. In particular, a new stepsize is derived by imposing finite termination on minimizing two dimensional strictly convex quadratic function. It is shown that, for the general quadratic function, the proposed stepsize asymptotically converges to the reciprocal of the largest eigenvalue of the Hessian. Furthermore, based on this spectral property, we propose a periodic gradient method by incorporating the Barzilai-Borwein method. Numerical comparisons with some recent successful gradient methods show that our new method is very promising.

Wednesday, November 20, 2019

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233

John Lien, Louisiana State University
TBD

Posted August 16, 2019

3:30 pm - 4:20 pm

Tao Mei, Balyor University
TBA

Thursday, November 21, 2019

Posted September 10, 2019

3:30 pm - 4:20 pm TBD

Leonid Berlyand, Department of Mathematics, Penn State University
TBD

Monday, November 25, 2019

Posted September 6, 2019

3:30 pm - 4:30 pm Lockett 233

Isaac Michael, Louisiana State University
TBA

Tuesday, December 3, 2019

Posted October 11, 2019

3:10 pm - 4:00 pm 285 Lockett

Kent Vashaw, Louisiana State University
TBA

Thursday, December 5, 2019

Posted September 13, 2019

3:30 pm - 4:20 pm TBD

Eric Rowell, Texas A&M
TBD