LSU
Mathematics

# Calendar

Time interval:   Events:

Tuesday, October 7, 2003

Posted October 1, 2003

3:30 pm - 4:30 pm Lockett 243

Patrick Gilmer, Mathematics Department, LSU
Integrality for TQFTs

Tuesday, October 28, 2003

Posted October 21, 2003

3:30 pm - 4:30 pm Lockett 243

Richard A. Litherland, Mathematics Department, LSU
On the Ozsvath-Szabo homology theory

Friday, November 7, 2003

Posted October 14, 2003

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

Charles Frohman, University of Iowa
Symplectic measure, Reidemeister torsion and the Jones polynomial

Monday, February 2, 2004

Posted January 27, 2004

3:30 pm - 4:30 pm Lockett 285

Tara Brendle, Department of Mathematics, LSU
On finite order generators of the mapping class group

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

Monday, February 16, 2004

Posted February 12, 2004

3:30 pm - 4:30 pm Lockett 285

Ian Agol, University of Illinois, Chicago
Tameness of hyperbolic 3-manifolds

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

Friday, March 12, 2004

Posted March 8, 2004

2:40 pm - 3:30 pm Lockett 381

Graham Denham, University of Western Ontario
The Homotopy Lie Algebra of an Arrangement

Monday, March 22, 2004

Posted March 3, 2004

3:40 pm - 4:30 pm tba

Neal Stoltzfus, Mathematics Department, LSU
Diagonalization of the Lickorish Form on Non-crossing Chord Diagrams

Monday, March 29, 2004

Posted March 22, 2004

3:30 pm - 4:30 pm 285 Lockett

Thomas Kerler, Ohio State University
Mapping Class Group Representations from TQFT

Abstract: The TQFTs of Witten Reshetikhin Turaev imply representations of the mapping class
groups over the cyclotomic integers Z[\zeta] for \zeta a prime root of unity. These
representations are highly structured and allow "perturbative" filtrations due to the
rich ideal structure of Z[\zeta]. It is not too surprising that they are related to
well known filtrations of the mapping class groups, given, for example, by the
Johnson subgroups. We will describe such explicit relations in "low order" examples.

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

Tuesday, September 14, 2004

Posted September 8, 2004

4:10 pm - 5:00 pm Lockett 284

Scott Baldridge, LSU
Introduction to 4-Manifold Theory, I

Tuesday, September 21, 2004

Posted September 20, 2004

4:10 pm - 5:00 pm Lockett 284

Scott Baldridge, LSU
Introduction to 4-manifold theory, II

Tuesday, September 28, 2004

Posted September 21, 2004

4:10 pm - 5:00 pm Lockett 284

Scott Baldridge, LSU
Introduction to 4-Manifolds III

Tuesday, October 12, 2004

Posted September 24, 2004

4:00 pm - 5:00 pm Lockett 284

Gregor Masbaum, University Paris 7
Integral lattices in TQFT

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

Wednesday, February 16, 2005

Posted February 10, 2005

1:00 pm - 2:00 pm Life Sciences A 663 Access Grid Video Conference Room

Daniel C. Cohen, Mathematics Department, LSU
Topology and Combinatorics of boundary manifolds of arrangements

Joint Virtual Seminar with the University of Iowa

Wednesday, February 23, 2005

Posted February 20, 2005

3:30 pm Lockett 285

William Schellhorn, LSU
Virtual Strings for Closed Curves with Multiple Components

Abstract: A Gauss paragraph is a combinatorial formulation of a generic closed curve with multiple components on some surface. A virtual string is a collection of circles with arrows that represent the crossings of such a curve. Every closed curve has an underlying virtual string and every virtual string has an underlying Gauss paragraph. A word-wise partition is a partition of the alphabet set of a Gauss paragraph that satisfies certain conditions with respect to the Gauss paragraph. This talk will discuss how the theory of virtual strings can be used to obtain necessary and sufficient conditions for a Gauss paragraph and word-wise partition to represent a closed curve in the 2-sphere.

Tuesday, March 8, 2005

Posted March 1, 2005

3:30 pm - 4:30 pm Lockett 239

Kee Lam, University of British Columbia
Low dimensional spinor bundles over projective spaces

Abstract: Given a k-dimensional vector bundle E over a
real projective space, the "geometric dimension problem" asks for the
maximal s such that E contains an s-dimensional trivial sub-bundle.
This problem originates from the study of immersions of projective
spaces into Euclidean space, and has been much pursued by topologists over
the last 40 years. As a general phenonmenon, k-s will be smaller
when k is divisible by a higher power of 2. In this talk we shall
examine such a phenonmenon from the view point of spinor representations,
and obtain some partial results. Some of these results turn out to be
best possible.

Tuesday, March 15, 2005

Posted March 9, 2005

4:00 pm - 5:00 pm Lockett 285

Patrick Gilmer, Mathematics Department, LSU
Integral Lattices in TQFT

Wednesday, March 30, 2005

Posted March 29, 2005

1:30 pm - 2:30 pm

Xiao-Song Lin, University of California Riverside
Representations of Braid Groups and Colored Homfly Polynomials

Virtual Seminar together with U Iowa

Monday, April 4, 2005

Posted March 29, 2005

3:30 pm - 4:30 pm Lockett 285

Khaled Qazaqzeh, LSU
Integral Bases for the SU(2)-TQFT-modules in genus one

Friday, April 15, 2005

Posted March 15, 2005

3:30 pm - 4:30 pm Life Science A663

Dror Bar-Natan, University of Toronto
I don't understand Khovanov-Rozansky homology

Abstract

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

Wednesday, April 20, 2005

Posted April 6, 2005

1:40 pm - 2:30 pm Life Science A 663

Cameron Gordon, University of Texas, Austin
Knots with Unknotting Number 1 and Conway Spheres

Virtual Seminar with U Iowa.
Cameron Gordon is visiting U Iowa.

Tuesday, April 26, 2005

Posted April 19, 2005

3:30 pm - 4:30 pm Lockett 285

Ambar Sengupta, Mathematics Department, LSU
Quantum Physics from Pure Logic

Friday, April 29, 2005

Posted March 27, 2005

3:30 pm - 4:30 pm Lockett 285

Abhijit Champanerkar, University of South Alabama
Scissors congruence and Bloch invariants of hyperbolic 3-manifolds.

Abstract: I will give a background of scissors congruence in various geometries. The complexified Dehn invariant for scissors congruence in hyperbolic 3-space gives rise to invariants of hyperbolic 3-manifolds called Bloch invariants introduced by Neumann and Yang. I will talk about the variation of the Bloch invariant and its relation to the PSL A-polynomial.

Tuesday, May 3, 2005

Posted April 27, 2005

4:00 pm - 5:00 pm Lockett 232

Tom Mark, Southeastern Louisiana University
Heegaard Floer invariants for fibered manifolds.

Heegaard Floer invariants, introduced by Ozsvath and Szabo several years ago,
are proving to be valuable tools in low-dimensional topology: in particular the theory
reproduces and extends many results obtained previously using Seiberg-Witten and/or Donaldson gauge theory, as well as yielding
novel results. I will discuss an ongoing project, joint with Slaven Jabuka,
whose goal is to understand the Ozsvath-Szabo invariants of Lefschetz fibered 4-manifolds. A natural place to start is to study the
Heegaard Floer homology groups of 3-manifolds that fiber over the circle,
particularly in terms of the
expression of their monodromy as a product of Dehn twists. We give some
preliminary results in this
area and indicate some directions for future work.

Tuesday, September 6, 2005

Posted August 16, 2005

4:10 pm - 5:00 pm Lockett 285

Non-cyclic covers of knot complements

Tuesday, September 13, 2005

Posted September 8, 2005

4:10 pm - 5:00 pm Lockett 285

Brendan Owens, LSU
Floer homology of double branched covers

Tuesday, September 20, 2005

Posted September 9, 2005

4:10 pm - 5:00 pm Lockett 285

Brendan Owens, LSU
Floer homology of double branched covers, Part II

Tuesday, September 27, 2005

Posted September 13, 2005

4:10 pm - 5:00 pm Lockett 285

Brendan Owens, LSU
Floer homology of double branched covers, Part III

Tuesday, October 4, 2005

Posted September 19, 2005

4:10 pm - 5:00 pm Lockett 285

Scott Baldridge, LSU
Symplectic 4-manifolds with prescribed fundamental group

Tuesday, October 11, 2005

Posted October 4, 2005

4:10 pm - 5:00 pm Lockett 285

Scott Baldridge, LSU
Symplectic 4-manifolds with prescribed fundamental group, Part II

Tuesday, October 18, 2005

Posted October 12, 2005

4:10 pm - 5:00 pm Lockett 285

Tara Brendle, Department of Mathematics, LSU
The Birman-Craggs-Johnson homomorphism and the homology of the Johnson Kernel

Tuesday, October 25, 2005

Posted October 12, 2005

4:10 pm - 5:00 pm 285 Lockett

Tara Brendle, Department of Mathematics, LSU
The Birman-Craggs-Johnson homomorphism and the homology of the Johnson Kernel, Part II

Tuesday, November 8, 2005

Posted November 1, 2005

4:10 pm - 5:00 pm Lockett 285

Tara Brendle, Department of Mathematics, LSU
The Birman-Craggs-Johnson homomorphism and the homology of the Johnson Kernel, Part III

Tuesday, November 29, 2005

Posted November 14, 2005

4:10 pm - 5:00 pm Lockett 285

Khaled Qazaqzeh, LSU
Integral Bases for Certain TQFT-Modules of the Torus

Tuesday, December 6, 2005

Posted November 20, 2005

4:10 pm - 5:00 pm 285 Lockett

Atle Hahn, University of Bonn and LSU
Towards a path integral derivation of the Reshetikhin-Turaev invariants

Tuesday, January 31, 2006

Posted January 24, 2006

4:30 pm - 5:30 pm Lockett 284

Daniel C. Cohen, Mathematics Department, LSU
tba

Tuesday, February 7, 2006

Posted January 26, 2006

4:40 pm - 5:30 pm Lockett 284

Neal Stoltzfus, Mathematics Department, LSU
Root Posets and Temperley-Lieb Algebras

Tuesday, February 14, 2006

Posted February 8, 2006

4:40 pm - 5:30 pm Lockett 284

Ben McReynolds, UT Austin
Separable subgroups of mapping class groups

Tuesday, March 7, 2006

Posted February 23, 2006

4:40 pm - 5:30 pm Lockett 284

Matilde Lalin, University of British Columbia
Some aspects of the Multivariable Mahler Measure

Tuesday, March 14, 2006

Posted March 9, 2006

4:40 pm - 5:30 pm Lockett 284

Patrick Gilmer, Mathematics Department, LSU
Lollipop trees in TQFT

Wednesday, April 26, 2006

Posted April 19, 2006

1:30 pm - 2:30 pm Life Science A663

David Futer, Michigan State University
"Geometry and combinatorics of arborescent link complements."

Virtual Seminar together with U Iowa

Tuesday, May 2, 2006

Posted April 16, 2006

4:40 pm - 5:30 pm Lockett 284

Alissa Crans, University of Chicago/Loyola Marymount University
Self-Distributivity in Coalgebras

Abstract: Self-distributive binary operations have appeared extensively in knot theory in recent years, specifically in algebraic structures called quandles.' A quandle is a set equipped with two binary operations satisfying axioms that capture the essential properties of the operations of conjugation in a group. The self-distributive axioms of a quandle correspond to the third Reidemeister move in knot theory. Thus, quandles give a solution to the Yang-Baxter equation, which is an algebraic distillation of the third Reidemeister move. We formulate analogues of self-distributivity in the categories of coalgebras and Hopf algebras and use these to construct additional solutions to the Yang-Baxter equation.

Tuesday, May 9, 2006

Posted May 1, 2006

3:40 pm - 4:30 pm Lockett 284

Abhijit Champanerkar, University of South Alabama
On the Mahler measure of Jones polynomials

Abtsract: We show that the Mahler measure of the Jones polynomial and of
the colored Jones polynomials converges under twisting for any link. In
terms of Mahler measure convergence, the Jones polynomial behaves like
hyperbolic volume under Dehn surgery. We also show that after
sufficiently many twists, the coefficient vector of the Jones polynomial
and of any colored Jones polynomial decomposes into fixed blocks
according to the number of strands twisted. We will also discuss recent

Tuesday, September 19, 2006

Posted September 5, 2006

4:40 pm - 5:30 pm Lockett 285

Patrick Gilmer, Mathematics Department, LSU
Surgery of type-p and quantum invariants of 3-manifolds

Tuesday, September 26, 2006

Posted September 6, 2006

4:40 pm - 5:30 pm Lockett 284

Neal Stoltzfus, Mathematics Department, LSU
Dessins in Knot Theory

Tuesday, October 3, 2006

Posted September 19, 2006

4:40 pm - 5:30 pm Lockett 284

David Cimasoni, UC Berkeley
Generalized Seifert surfaces and signatures of colored links

The Seifert surface is a well-known and very useful tool in link theory.
For instance, it permits to study the Alexander invariants, the Conway
polynomial, and the signature of an oriented link. In this talk, we
shall
introduce 'generalized Seifert surfaces' for colored links. They
provide a
geometric interpretation of the multivariable Alexander invariants
and of
the Conway potential function. They also make it possible to define (and
compute easily) a multivariable signature that generalizes the
Levine-Tristram signature. This multivariable signature turns out to
be a slight generalization of invariants introduced by P. Gilmer and L. Smolinsky.

Tuesday, October 10, 2006

Posted October 4, 2006

4:40 pm - 5:30 pm Lockett 284

Neal Stoltzfus, Mathematics Department, LSU
Skein Modules of Cylinders and Quantum Cluster Algebras

Friday, October 13, 2006

Posted October 4, 2006

3:40 pm - 4:30 pm Lockett 284

Indira Lara Chatterji, Ohio State University
A characterization of hyperbolicity.

Tuesday, October 24, 2006

Posted October 17, 2006

4:40 pm - 5:30 pm Lockett 284

Brendan Owens, LSU
Knot surgeries and negative definite four manifolds

Tuesday, November 7, 2006

Posted October 25, 2006

4:40 pm - 5:30 pm Lockett 284

Matilde Lalin, University of British Columbia
Functional equations for the Mahler measure of genus 1 curves

Thursday, November 9, 2006

Posted November 3, 2006

11:00 am - 12:00 pm Johnston 338

Ronald Fintushel, Michigan State University
Surgery on Nullhomologous Tori

Virtual Seminar together with Rice University

Monday, November 13, 2006

Posted November 3, 2006

4:40 pm - 5:30 pm Lockett 284

Matthew Hedden, M.I.T.
The meaning and comparison of smooth concordance invariants

Abstract: In the past three years, several new invariants of smooth knot concordance have been discovered. This lecture will focus on two of these invariants, denoted $tau(K)$ and $s(K)$, respectively. Here $K$ denotes a knot in the three-sphere. The former invariant was discovered by Ozsvath and Szabo and independently by Rasmussen and is defined using the Floer homology theory for knots introduced by the aforementioned authors. $s(K)$ was introduced by Rasmussen and is defined in the context of Khovanov knot homology. The invariants share several formal properties and agree for many knots. In particular, each invariant is a homomorphism from the smooth knot concordance group to the integers, and each bounds the smooth four-genus, $g_4(K)$. Moreover, each invariant can be used to determine the smooth four-genera of torus knots and provide new proofs of Milnor's famous conjecture on the four-genera and unknotting numbers of these knots. It was conjectured by Rasmussen that $2tau$ and $s$ agree for all knots. If confirmed, this conjecture would point to a surprising connection between the analytically defined Ozsvath-Szabo homology theory and the combinatorially defined Khovanov homology. Moreover, it would seem to indicate a relationship between the gauge theory of three and four-manifolds and the quantum framework underlying the Jones polynomial. This lecture will explore Rasmussen's conjecture by discussing evidence for its validity and families of knots for which the conjecture holds. In this pursuit, it will be appropriate to briefly comment on the geometry contained by the $tau$ invariant - in particular I'll discuss a theorem which indicates that $tau$ can be used to detect when a knot arises as the intersection of a complex curve in $C^2$ with the three-sphere. This connection partially arises with the $s$ invariant. The main purpose, however, wil be to present the first counterexamples to Rasmussen's conjecture, discovered last year by myself and Philip Ording. The examples come from the Whitehead double construction. I will try to say some words about how Rasmussen's conjecture, though false, could be interpreted in the context of a larger conjecture connecting Floer homology to Khovanov homology, also due to Rasmussen.

Tuesday, January 30, 2007

Posted January 10, 2007

4:40 pm - 5:30 pm Lockett 276

Emille K. Davie, University of Georgia
Characterizing Right-Veering Surface Diffeomorphisms Via the Burau Representation

Tuesday, March 27, 2007

Posted March 7, 2007

4:40 pm - 5:00 pm Lockett 276

Kathy Zhong, Cal State Sacramento
Calculate Kauffman Polynomials of some Knots Using Kauffman Skeins

Thursday, March 29, 2007

Posted March 21, 2007

11:00 am Lockett 381 Originally scheduled for 4:40 pm, Wednesday, March 28, 2007

Stephen Bigelow, UC Santa Barbara
Representations of Planar Algebras

Time/Date Changed

Tuesday, September 4, 2007

Posted August 27, 2007

5:10 pm - 6:00 pm Lockett 276

Adam Lowrance, Department of Mathematics, Vassar College
On Knot Floer Width and Turaev Genus

Monday, September 10, 2007

Posted September 5, 2007

4:30 pm - 5:30 pm Lockett 276

Steve Wallace, LSU
Surgery untying of knots

Wednesday, September 12, 2007

Posted September 7, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Moshe Cohen, Department of Mathematics, Bar-Ilan University, Israel
Introductory remarks on Khovanov homology

This is a virtual topology seminar together with U Iowa

Monday, September 17, 2007

Posted September 7, 2007

4:40 pm - 5:30 pm Lockett 276

Hee Jung Kim, Department of Mathematics, LSU
Topological triviality of smoothly knotted surfaces in 4-manifolds

Wednesday, September 19, 2007

Posted September 13, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Neal Stoltzfus, Mathematics Department, LSU
Quasi-Trees and Khovanov homology

Virtual Seminar together with U Iowa

Monday, September 24, 2007

Posted September 19, 2007

4:40 pm - 5:30 pm Lockett 276

Scott Baldridge, LSU
A symplectically aspherical manifold with b_1=1

Wednesday, September 26, 2007

Posted September 24, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Adam Lowrance, Department of Mathematics, Vassar College

Monday, October 1, 2007

Posted September 24, 2007

4:40 pm - 5:30 pm Lockett 276

Scott Baldridge, LSU
A symplectically aspherical manifold with b_1=1, Part II

Wednesday, October 3, 2007

Posted September 24, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Adam Lowrance, Department of Mathematics, Vassar College

Virtual Seminar together with U Iowa

Wednesday, October 10, 2007

Posted October 1, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Moshe Cohen, Department of Mathematics, Bar-Ilan University, Israel
On a result of Ozsvath and Manolescu

Virtual Seminar together with U Iowa

Monday, October 15, 2007

Posted October 2, 2007

4:40 pm - 5:30 pm Lockett 276

Neal Stoltzfus, Mathematics Department, LSU
The Bollobas-Riordan-Tutte polynomial as a tri-graded Poincare-polynomial (due to N. Forman)

Wednesday, October 17, 2007

Posted October 3, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

John Etnyre, Georgia Institute of Technology
A geometric reason for the non-sharpness of Bennequin's inequality for some fibered knots

Virtual Seminar together with U Iowa

Monday, October 22, 2007

Posted October 22, 2007

4:40 pm - 5:30 pm Lockett 276

Neal Stoltzfus, Mathematics Department, LSU
The Bollobas-Riordan-Tutte polynomial as a tri-graded Poincare-polynomial (due to N. Forman), Part II

Wednesday, October 24, 2007

Posted October 22, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Charles Frohman, University of Iowa
On Bar-Natan's skein module

Virtual Seminar together with U Iowa (talk this week is from Iowa)

Monday, October 29, 2007

Posted October 24, 2007

4:40 pm - 5:30 pm Lockett 276

Ambar Sengupta, Mathematics Department, LSU
Gaussian Matrix Integrals

Abstract: The talk of the same title given in the probability seminar concluded with a definition of a who a topologist is. In this talk we will strive to define a probabilist. Along the way we shall examine the representation of Gaussian integrals of matrix-trace functions in terms of sums over surfaces of varying genus. This is an illustration of a broader phenomenon of integrals arising from physical theories having topological interpretations.

Wednesday, October 31, 2007

Posted October 25, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Jeff Boerner (U Iowa): On the Asaeda-Przytycki-Sikora homology

Virtual Seminar together with U Iowa (talk this week is from Iowa)

Thursday, November 1, 2007

Posted October 25, 2007

12:40 pm - 1:30 pm tba

Junior Topology Seminar

This is a reading seminar. See this announcement

Wednesday, November 7, 2007

Posted November 4, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Heather Russell (U Iowa): Embedded Khovanov homology of S^1\times D^2 and the homology of the (n,n)-Springer Fiber

Virtual Seminar together with U Iowa (talk this week is from Iowa)

Thursday, November 8, 2007

Posted November 6, 2007

12:40 pm - 1:30 pm Lockett 119

Junior Topology Seminar

Monday, November 12, 2007

Posted November 6, 2007

4:40 pm - 5:30 pm Lockett 276

Patrick Gilmer, Mathematics Department, LSU
Congruence and quantum invariants

Wednesday, November 14, 2007

Posted November 6, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Steve Wallace, LSU
Surgery equivalence invariants of colored knots

Virtual Seminar together with U Iowa

Thursday, November 15, 2007

Posted November 6, 2007

12:40 pm - 1:30 pm Lockett 119

Junior Topology Seminar

Wednesday, November 21, 2007

Posted November 6, 2007

3:40 pm - 4:30 pm

NO VIRTUAL SEMINAR (THANKSGIVING)

Wednesday, November 28, 2007

Posted November 6, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663

Adam Lowrance, Department of Mathematics, Vassar College
On a paper by Ozsvath, Rasmussen and Szabo on the odd Khovanov homology

Virtual Seminar together with U Iowa

Wednesday, January 23, 2008

Posted January 21, 2008

3:30 pm - 4:30 pm Bio. Sciences Annex, A663

Charles Frohman, University of Iowa
An introduction to Frobenius extensions and TQFT over rings

Virtual Seminar together with UIowa

Wednesday, January 30, 2008

Posted January 22, 2008

3:30 pm - 4:30 pm Bio. Sciences Annex, A663

Charles Frohman, University of Iowa
sl_3 Topological Quantum Field Theory after Khovanov

Virtual Seminar together with UIowa

Wednesday, February 13, 2008

Posted January 24, 2008

3:30 pm - 4:30 pm Bio. Sciences Annex, A663

Adam McDougall (Virtual Seminar together with UIowa)

Wednesday, February 20, 2008

Posted January 24, 2008

3:30 pm - 4:30 pm Bio. Sciences Annex, A663

Hee Jung Kim, Department of Mathematics, LSU
Embeddings of Surfaces in 4-manifolds

(Virtual Seminar together with UIowa)

Monday, February 25, 2008

Posted January 30, 2008

3:40 pm - 4:30 pm Lockett 276

Gregor Masbaum, University Paris 7
TQFT and the Nielsen-Thurston classification of surface homeomorphisms

Wednesday, March 5, 2008

Posted February 20, 2008

3:30 pm - 4:30 pm Bio. Sciences Annex, A663

Alissa Crans, University of Chicago/Loyola Marymount University
2-groups: Categorified groups

(Virtual Seminar together with UIowa; the talk is broadcasted from Iowa)

Wednesday, March 26, 2008

Posted February 20, 2008

3:30 pm - 4:30 pm Bio. Sciences Annex, A663

Hee Jung Kim, Department of Mathematics, LSU
Knotting Surfaces in 4-manifolds, Part II

(Virtual Seminar together with UIowa)

Monday, March 31, 2008

Posted January 24, 2008

3:40 pm - 4:30 pm Lockett 276

Charles Livingston, Indiana University
Twisted Alexander polynomials, metabelian representations, and the knot slicing problem

Wednesday, April 2, 2008

Posted February 20, 2008

3:30 pm - 4:30 pm Bio. Sciences Annex, A663

Models for evaluating the Homfly polynomial

Anna Meyers (UIowa) (Virtual Seminar together with UIowa)

Wednesday, April 9, 2008

Posted April 7, 2008

3:30 pm - 4:30 pm Bio. Sciences Annex, A663

Cody Armond, Department of Mathematics, LSU
On the Huynh-Le Quantum Determinant for the Colored Jones Polynomial

(Virtual Seminar together with UIowa)

Friday, April 11, 2008

Posted February 18, 2008

3:40 pm - 4:30 pm Lockett 276

Oleg Viro, SUNY Stony Brook
Twisted acyclicity of circle and link signatures

Monday, April 28, 2008

Posted February 27, 2008

3:40 pm - 4:30 pm Lockett 276

Joan Birman, Columbia University/Barnard College Receipient of the Chauvenet Prize
Twisted torus knots and Lorenz knots

Wednesday, August 27, 2008

Posted August 22, 2008

3:40 pm X-lab

Test run for Virtual Seminar

Participating Universities: LSU, U Iowa, GWU, U Miami

Wednesday, September 10, 2008

Posted September 10, 2008

3:30 pm - 4:30 pm X-lab: Lockett 233

Heather Russell, USC
Virtual Seminar

Live from Iowa City

Wednesday, September 24, 2008

Posted September 23, 2008

3:40 pm - 4:30 pm X-lab: Lockett 233

Hee Jung Kim, Department of Mathematics, LSU
tba

Virtual Seminar together with UIowa and the University of Miami

Wednesday, October 1, 2008

Posted October 1, 2008

3:40 pm - 4:30 pm X-lab: Lockett 233

Virtual Seminar with UIowa/UMiami

Wednesday, October 8, 2008

Posted October 1, 2008

3:40 pm - 4:30 pm X-lab: Lockett 233

Virtual Seminar with UIowa/UMiami

Ken Baker (University of Miami)

Wednesday, November 19, 2008

Posted November 17, 2008

3:40 pm - 4:30 pm X-lab: Lockett 233

Lawrence Roberts, Michigan State University
Knot Floer homology for some fibered knots

Abstract: I will talk about a computing the
knot Floer homology of a class of fibered knots in
rational homology spheres, for which the computation is
particularly simple.

Joint virtual seminar with UIowa, Rice, UMiami, Boise State, GWU

Wednesday, December 3, 2008

Posted December 2, 2008

3:40 pm - 4:30 pm X-lab: Lockett 233

Leah Childers, LSU
Birman-Craggs-Johnson Homomorphism of the Torelli Group

Virtual Seminar together with UIowa, Rice University, UMiami, Boise State University, George Washington University

Wednesday, February 11, 2009

Posted February 10, 2009

3:40 pm - 4:40 pm Lockett 233

Virtual Seminar: Unstable Vassiliev Theory

This week's AccessGrid virtual seminar will be presented locally by Chad Giusti. For more information and for future event listings, please visit the Topology Seminar events page.

Wednesday, February 18, 2009

Posted February 17, 2009

3:30 pm - 4:30 pm 233 Lockett

Scott Baldridge, LSU
Virtual Seminar: Cube knots and knot Floer homology from cube diagrams

This week's AccessGrid virtual seminar will be presented locally by Scott Baldridge. For more information and for future event listings, please visit the Topology Seminar events page.

Monday, March 22, 2010

Posted March 11, 2010

3:40 pm - 5:00 pm Lockett 276

Gregor Masbaum, University Paris 7
The Arf-invariant formula for graphs on surfaces

Abstract:
Kasteleyn showed how to count dimer coverings (= perfect matchings) on
a planar bipartite graph by evaluating the determinant of a certain
matrix. The method works for non-bipartite graphs as well, upon
replacing the determinant with a Pfaffian. If the graph is not planar,
but embedded in a surface of genus g, Kasteleyn stated and
Gallucio-Loebl proved a formula expressing the number of dimer
coverings as a linear combination of 4^g Pfaffians. The main aim of
the talk is to explain a new proof of this formula based on the theory
of Arf invariants of quadratic forms on the mod 2 homology of the
surface. I will then discuss the question of whether the minimal
number of Pfaffians nedded to count dimer coverings is always a power
of 4. If time remains, I will explain a recent result of Loebl and
myself which gives an affirmative answer to the analogous question for
the Ising model on a graph.

Thursday, July 1, 2010

Posted June 28, 2010

10:30 am - 11:30 am Lockett 233

Paul Kirk, Indiana University
Untwisted Whitehead doubles of $(2, 2^k-1)$ torus knots are linearly independent in the smooth knot concordance group.

Abstract: We revisit an argument of Furuta, using SO(3) instanton moduli spaces on 4-manifolds with boundary and estimates of Chern-Simons invariants of flat SO(3) connections on 3-manifolds, to prove that the infinite family of untwisted positive clasped Whitehead doubles of the $(2, 2^k-1)$ torus knots are linearly independent in the smooth knot concordance group. (joint work with Matt Hedden)

Tuesday, March 29, 2011

Posted March 18, 2011

3:40 pm - 4:30 pm 276 Lockett

Kate Kearney, Indiana University
An Obstruction to Knots Bounding Moebius Bands

Wednesday, August 24, 2011

Posted August 18, 2011

3:40 pm - 4:30 pm Locket 233

Charles Frohman, University of Iowa
Virtual Seminar: Projective Representations of the Mapping Class group of a surface with boundary coming from TQFT

(Joint with Joanna Kania-Bartoszynska and Mike Fitzpatrick)

Abstract:
For each odd prime p, and primitive 2pth root unity, there is a projective representation of the mapping class group of a torus
of dimension 2, that comes from the projective action of the mapping class group of a one punctured torus ( aka the modular group)
on a portion of the state space assigned to a once punctured torus. I will prove up to conjugacy, this family extends to a continuous
family of representations of the modular group defined on the unit circle. This family includes a twisted version of the canonical representation of
the modular group.
This means that the dilation coefficient of pseudo-anosov mapping classes can be computed as a limit of quantum invariants of mapping tori.
It also means that the hyperbolic volume should also be computable, though the connection is less direct.

Wednesday, September 14, 2011

Posted August 29, 2011

3:40 pm - 4:30 pm Locket 233

Greg Muller, Department of Mathematics, LSU
Virtual Seminar: Skein algebras of marked surfaces

Abstract: Given a surface with boundary and a collection of marked points on the boundary, one may consider all curves in the surface which end at the marked points. One may define the Kauffman skein algebra (at q=1) generated by these curves; this generalizes the unmarked' definition where only loops are allowed. Generalizing results of Bullock, Barrett and Przytycki-Sikora, this algebra can be realized as the algebra of functions on a space of (twisted) SL_2(C) local systems with extra data at the marked points. Additionally, new phenomena arise in the marked case which do not generalize any unmarked results. When there are enough marked points for the surface to admit a triangulation, then each triangulation gives an embedding of the skein algebra into a ring of Laurent polynomials. Through these embeddings, it can be shown that the skein algebra coincides with the upper cluster algebra' of the marked surface, an algebra with significance in combinatorics, Lie theory and Teichmuller theory. Part of this work is joint with Peter Samuelson.

Wednesday, September 28, 2011

Posted September 9, 2011

3:40 pm - 4:30 pm Lockett 233

Shin Satoh, Kobe University
Virtual Seminar: Quandle cocycle invariants of roll-spun knots

Abstract We have two fundamental families in 2-knot theory; one is a ribbon 2-knot and the other is a deform-spun knot. Since any ribbon 2-knot is represented by a diagram with no triple point, the quandle cocycle invariant is always trivial. As special families of deform-spun knots, we have twist-spun knots and roll-spun knots. The invariant of a twist-spun knot have been studied in many papers. The aim of this talk is to explain how to calculate the quandle cocycle invariant of a roll-spun knot and give several properties.

Wednesday, October 5, 2011

Posted August 29, 2011

3:40 pm - 4:30 pm Locket 233

Trenton Schirmer, Department of Mathematics, University of Iowa
Virtual Seminar: The degeneration ratio of tunnel number under connect sum

The tunnel number $t(L)$ of a link $L$ in $S^3$ is the minimal number of arcs ${t_1, .... , t_n}$ that can be embedded in the closure of $S^3-N(L)$ so that S^3-N(L cup t_1 cup ... cup t_n is a handlebody. When $L$ is a knot $t(K)+1$ is just the Heegaard genus of its complement. The `degeneration ratio'' of a connect sum $L =L_1$ # $L_2$ is defined as t L/(t(L_1)+t(L_2)). We give some new examples of links for which the degeneration ratio becomes low.

Wednesday, October 19, 2011

Posted September 11, 2011

3:40 pm - 4:30 pm Lockett 233

Eamonn Tweedy, Department of Mathematics, Rice University
Virtual Seminar: A filtration on the Heegaard Floer chain complex of a double branched cover

Abstract: Seidel and Smith defined their fixed-point symplectic Khovanov cohomology theory for links in the 3-sphere. For the case of a knot K, they described how to define a particular filtration on their complex. Via an observation of Manolescu, this filtration induces a spectral sequence from the Seidel-Smith theory to the Heegaard Floer hat theory for the double cover of the 3-sphere branched along K. This spectral sequence is itself a knot invariant, and has some nice properties. We also discuss how the construction leads to a family of rational-valued knot invariants.

Wednesday, October 26, 2011

Posted September 8, 2011

3:40 pm - 4:30 pm Lockett 233

Effie Kalfagianni, Michigan State University
Virtual Seminar: Polyhedral decompositions, essential surfaces and colored Jones polynomials.

Abstract: We generalize the checkerboard decompositions of alternating knots and links: For A- or B-adequate diagrams, we show that the checkerboard knot surfaces are incompressible, and we obtain an ideal polyhedral decomposition of their complement. In the talk I will describe these decompositions and give some of the applications, which include fibering knot criteria and relations between hyperbolic volume and colored Jones polynomials. The talk will be based on joint work with Dave Futer (Temple) and Jessica Purcell (BYU).

Wednesday, November 2, 2011

Posted September 23, 2011

3:40 pm - 4:30 pm Lockett 233

Adam Lowrance, Department of Mathematics, Vassar College
Virtual Seminar: "A categorification of the Tutte polynomial"

Abstract: The Tutte polynomial is a graph and matroid polynomial which has a close relationship with the Jones polynomial. We construct a categorification of the Tutte polynomial for graphs and matroids. Our construction is modeled after the construction of odd Khovanov homology, which is a categorification of the Jones polynomial developed by Ozsvath, Rasmussen, and Szabo. Many properties of the Tutte polynomial lift to expected properties of our categorification. The deletion-contraction relation of the Tutte polynomial becomes an exact triangle in the categorification, and the formula for the Tutte polynomial of the dual matroid has an analog for our categorification. We will also present examples and an application that leads to an invariant of (mutation classes of) alternating links.

Wednesday, November 9, 2011

Posted November 4, 2011

3:40 pm - 4:30 pm In R^4

Scott Baldridge, LSU
Knotted embedded tori in R^4

Abstract: One of the barriers to studying knotted surfaces in R^4 has been that there are few ways to represent them that lead to powerful yet easy-to-compute invariants. In this talk we will describe a new way to represent 2-dimensional knotted tori in R^4 using 4n half-integer valued points in the cube [0,n]^4. We will illustrate why the construction represents knotted spun tori and discuss the ramifications of the representation to topics such as Heegaard Floer Homology and Contact Homology.

Wednesday, November 16, 2011

Posted September 23, 2011

3:40 pm - 4:30 pm Lockett 233

Heather Russell, USC
Virtual Seminar: Springer varieties and spider webs

Abstract: Springer varieties are certain flag varieties classically studied because their cohomology rings are Weyl group representations. Khovanov, Stroppel-Webster, Cautis-Kamnitzer, Seidel-Smith and others have studied the connections of Springer varieties to knot theory. In past work we built on ideas of Khovanov and Stroppel-Webster to give a diagrammatic framework enabling the study of Springer representations as well as the topology of certain Springer varieties via sl_2 webs. We will discuss recent work extending some of these results to other classes of Springer varieties using sl_3 webs.

Wednesday, November 30, 2011

Posted October 31, 2011

3:40 pm - 4:30 pm Lockett 233

Ben McCarty, LSU
Virtual Seminar: "On the rotation class of knotted Legendrian tori in R^5"

Abstract Legendrian knots in R^3 have been studied extensively in recent years. However, much less is known about Legendrian knots in higher dimensions. We present Lagrangian hypercube diagrams as a convenient tool to study knotted Legendrian tori in R^5 with the standard contact structure. In particular, we describe an easy way to compute a Legendrian invariant, the rotation class, from a Lagrangian hypercube diagram, and discuss applications to contact homology. (Joint work with S. Baldridge)

Wednesday, January 11, 2012

Posted December 21, 2011

3:40 pm - 4:30 pm Lockett 233

Benjamin Himpel, Centre for Quantum Geometry of Moduli Spaces, Aarhus, Denmark
tba

Wednesday, January 25, 2012

Posted January 11, 2012

3:40 pm - 4:30 pm Lockett 233

Yeonhee Jang, Hiroshima University
Virtual Seminar: Bridge presentations of links

Abstract: This talk will be devoted to introduce the speaker's works related to bridge presentations of links. In the first half of this talk, we introduce results on the classification or characterization of certain 3-bridge links and their 3-bridge presentations. In the last half, we introduce results on Cappell-Shaneson's question which asks whether the bridge numbers of links are equal to the minimal numbers of meridian generators of link groups.

Wednesday, February 1, 2012

Posted January 28, 2012

3:40 pm - 4:30 pm Lockett 233

Cody Armond, Department of Mathematics, LSU

Wednesday, February 15, 2012

Posted February 6, 2012

3:40 pm - 4:30 pm Lockett 233

Dan Rutherford, University of Arkansas
A combinatorial Legendrian knot DGA from generating families

Abstract: This is joint work with Brad Henry. A generating family for a Legendrian knot L in standard contact R^3 is a family of functions f_x whose critical values coincide with the front projection of L. Pushkar introduced combinatorial analogs of generating families which have become known as Morse complex sequences. In this talk, I will describe how to associate a differential graded algebra (DGA) to a Legendrian knot with chosen Morse complex sequence. In addition, I will discuss the geometric motivation from generating families and the relationship with the Chekanov-Eliashberg invariant.

Wednesday, March 14, 2012

Posted February 26, 2012

3:40 pm - 4:30 pm Lockett 233

John Etnyre, Georgia Institute of Technology
Virtual Seminar: Open books decompositions and the geometry of contact structures

Abstract: Giroux's correspondence between open books decompositions and contact structures on 3-manifolds has been key to many advances in contact geometry and its application to topology. In this talk I will discuss several recent advances that describe how properties of a contact structure, such as tightness and fillability, are reflected in its associated open book decompositions and vice vera. In addition I will discuss how some operations on open books decompositions, such as cabling a binding component, affect the associated contact structure.

Wednesday, March 21, 2012

Posted March 7, 2012

3:40 pm - 4:30 pm Lockett 233

Matt Clay, Allegheny College
Virtual Seminar: The geometry of right-angled Artin subgroups of mapping class groups

Abstract: We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. This is joint work with Chris Leininger and Johanna Mangahas.

Wednesday, April 25, 2012

Posted April 9, 2012

3:40 pm - 4:30 pm Lockett 233

Rafal Komendarczyk, Tulane University
Virtual Seminar: "Towards the $\kappa$--invariant conjecture"

Abstract: A parametrization of an $n$-component link in $R^3$, produces a natural evaluation map from the $n$-torus to the configuration space of $n$ distinct points in $R^3$. Denote by $\kappa$ the map from homotopy links to the set of homotopy classes of evaluation maps. A natural conjecture arises, that $\kappa$ classifies homotopy links. Koschorke first proved that $\kappa$ has this property for homotopy Brunnian links. In this talk, I will show how to recast Koschorke's correspondence in the language of torus homotopy groups, which reveals an interesting algebraic structure. Further, time permitting, I will describe progress towards extending the result beyond the Brunnian case. This is joint work with Frederick Cohen at Rochester and Clayton Shownkwiler at UGA.

Wednesday, May 9, 2012

Posted April 3, 2012

3:40 pm - 4:30 pm Lockett 233 Originally scheduled for 4:40 pmWednesday, April 4, 2012

Dennis Roseman
Small Lattice Surfaces in Four Dimensions

Abstract: A lattice point is a point with integer coordinates. The standard p x q x r x s lattice box is all lattice points in R^4 within [0,p-1] x [0,q-1] x [0, r-1] x [0, s-1]. A lattice square in R^4 is a unit square whose vertices are lattice points. A lattice surface or lattice surface link is a finite union of lattice squares which is topologically is a closed two-dimensional manifold (perhaps not connected, perhaps not orientable).
We focus on the question: which surface link types can be represented as lattice surfaces in a given small lattice box? We show that any orientable surface link in a 3x3x3x3 lattice box is a pseudo-ribbon link, and discuss a new surface link invariant that can detect non-psuedo-ribbon links. We give a table of surface links that lie in a 3x3x3x2 lattice box and develop notations, terminology, mathematical strategies and visualization tools for investigating these and surface links in slightly larger boxes.

Wednesday, September 5, 2012

Posted August 26, 2012

3:30 pm - 4:20 pm

Virtual Seminar: "Hyperbolic structures from link diagrams"

W. Thurston demonstrated that every link in $S^3$ is a torus link, a satellite link or a hyperbolic link and these three categories are mutually exclusive. It also follows from work of W. Menasco that an alternating link represented by a prime diagram is either hyperbolic or a $(2,n)$--torus link. The talk will introduce an alternative method for computing the hyperbolic structure of the complement of a hyperbolic link. It allows computing the structure directly from the link diagram. Some of its consequences will be discussed, including a surprising rigidity property of certain tangles, and the formulas that allow one to calculate the exact hyperbolic volume, as well as complex volume, of hyperbolic 2--bridge links. This is joint work with M. Thistlethwaite.

Wednesday, September 19, 2012

Posted August 21, 2012

3:30 pm - 4:20 pm Lockett 233 Originally scheduled for 4:40 pmSunday, September 2, 2012

Shea Vela-Vick, Louisiana State University
Virtual Seminar: "The equivalence of transverse link invariants in knot Floer homology"

Abstract: The Heegaard Floer package provides a robust tool for studying contact 3-manifolds and their subspaces. Within the sphere of Heegaard Floer homology, several invariants of Legendrian and transverse knots have been defined. The first such invariant, constructed by Ozsvath, Szabo and Thurston, was defined combinatorially using grid diagrams. The second invariant was obtained by geometric means using open book decompositions by Lisca, Ozsvath, Stipsicz and Szabo. We show that these two previously defined invariant agree. Along the way, we define a third, equivalent Legendrian/transverse invariant which arises naturally when studying transverse knots which are braided with respect to an open book decomposition.

Wednesday, October 3, 2012

Posted September 1, 2012

3:30 pm - 4:20 pm

Ken Baker, University of Miami
Virtual Seminar: "Annular twists and Bridge numbers of knots"

Abstract: Performing +1/n and -1/n Dehn surgery on the boundary components of an annulus A in a 3-manifold M provides a homeomorphism of M similar to a Dehn twist. If a knot intersects the interior of A in an essential manner, then this twisting produces an infinite family of knots. In joint work with Gordon and Luecke, we show (under certain hypotheses) that if the bridge numbers of this family with respect to a given Heegaard surface of M are bounded, then the annulus may be isotoped to embed in the Heegaard surface. With this we construct genus 2 manifolds that each contain a family of knots with longitudinal surgeries to S^3 and unbounded genus 2 bridge number. In contrast, our earlier work gives an a priori upper bound on the bridge number of a knot in a genus g manifold with a non-longitudinal S^3 surgery.

Wednesday, October 10, 2012

Posted September 14, 2012

3:30 pm - 4:20 pm

Moshe Cohen, Department of Mathematics, Bar-Ilan University, Israel
Virtual Seminar: "Kauffman's clock lattice as a graph of perfect matchings: a formula for its height"

Abstract: Kauffman gives a state sum formula for the Alexander polynomial of a knot using states in a lattice that are connected by his clock moves. We show that this lattice is more familiarly the graph of perfect matchings of a bipartite graph obtained from the knot diagram by overlaying the two dual Tait graphs of the knot diagram. Using a partition of the vertices of the bipartite graph, we give a direct computation for the height of Kauffman's clock lattice obtained from a knot diagram with two adjacent regions starred and without crossing information specified. We prove structural properties of the bipartite graph in general and mention applications to Chebyshev or harmonic knots (obtaining the popular grid graph) and to discrete Morse functions.

Wednesday, October 17, 2012

Posted September 14, 2012

3:30 pm - 4:20 pm

Adam Lowrance, Department of Mathematics, Vassar College
Virtual Seminar: "Khovanov homology and oriented ribbon graphs"

Abstract: We define Khovanov homology of ribbon graphs and discuss how it ties together the Khovanov homology of both classical and virtual links. The spanning tree complex of Khovanov homology generalizes in the ribbon graph setting to a quasi-tree complex, which shows a relation between the Khovanov homology (of both classical and virtual links) and Turaev genus. We also discuss ribbon graph Reidemeister moves and discuss how they may be used to give distinct virtual links with isomorphic Khovanov homology.

Wednesday, October 24, 2012

Posted September 19, 2012

3:30 pm - 4:20 pm Lockett 233

Bulent Tosun, CIRGET (Montreal)
Virtual Seminar: "Cabling and Legendrian simplicity"

Abstract:

This talk will be about Legendrian and transverse knots in cabled knot types in standard contact three sphere and their classifications up to contact isotopy. We will be able to give structural theorems that ensure when cables a of a Legendrian simple knot type are Legendrian simple. We will then give complete classification in case of cables of positive torus knots. These results exhibits many new phenomena about structural understanding of Legendrian and tansverse knot theory. The key ingredient of the proofs will be understanding of certain quantities associated to contact solid tori representing positive torus knots in standard contact three sphere. Part of the results are joint work with John Etnyre and Douglas LaFountain.

Wednesday, January 23, 2013

Posted December 3, 2012

3:30 pm - 4:20 pm Lockett 233

Doug LaFountain, Western Illinois University
Virtual Seminar: "Links and doubling branched surfaces"

Abstract: We consider oriented links in the 3-sphere which are braided positively with respect to two different braid fibrations, and hence represent two different braid conjugacy classes for the link type. Following work of Morton, we show that these two braid fibrations may be assumed to be mutually braided with respect to each other; furthermore, after isotopies of the link which are non-increasing on braid index, the link projects onto one of a family of well-defined branched surfaces in the complement of the braid axes. Time permitting we discuss potential applications; this is joint work with Bill Menasco and Hiroshi Matsuda.

Wednesday, January 30, 2013

Posted December 3, 2012

3:30 pm - 4:20 pm Lockett 233

Steven Sivek, Harvard
Virtual Seminar: "Donaldson invariants of symplectic manifolds"

Abstract: Donaldson proved in the late 80s that his polynomial invariants of smooth 4-manifolds are nonzero for Kaehler surfaces, and this was only recently extended to symplectic manifolds by Kronheimer and Mrowka. In this talk, we will give a new proof that symplectic 4-manifolds have nonzero Donaldson invariants. Our proof will rely on Kronheimer and Mrowka's structure theorem for manifolds of "simple type" together with some known cases of Witten's conjecture relating the Donaldson and Seiberg-Witten invariants.

Wednesday, February 6, 2013

Posted December 3, 2012

3:30 pm - 4:20 pm Lockett 233

Tye Lidman, UT Austin
Virtual Seminar: "Left-orderability and Floer homology"

Abstract: We will study the seemingly unnatural question of when the fundamental group of a three-manifold can be given a left-invariant order. This is related to the existence of taut foliations on the manifold as well as the structure of its Heegaard Floer homology groups.

Wednesday, February 13, 2013

Posted January 22, 2013

3:30 pm - 4:20 pm Lockett 233

Anne Thomas, University of Sydney
Virtual Seminar: "Infinite reduced words and the Tits boundary of a Coxeter group"

Abstract: Let (W,S) be a Coxeter system with W infinite. An infinite reduced word of W is an infinite sequence of elements of S such that each finite subsequence is a reduced word. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex of W. We consider many special cases, including W word hyperbolic and X with isolated flats. This is joint work with Thomas Lam.

Wednesday, March 13, 2013

Posted January 22, 2013

3:30 pm - 4:20 pm Lockett 233

Clayton Shonkwiler, University of Georgia
Virtual Seminar: "The geometry and topology of random polygons"

Abstract: What is the expected shape of a random closed curve in space? For example, what is the expected radius of gyration or expected total curvature? What is the likelihood that the curve is knotted? As a first step, what are the corresponding answers when I restrict to closed n-gons in space? Aside from purely mathematical interest, such questions are natural in the context of statistical physics since n-gons in space are simple models for ring polymers with n monomers in solution. When we restrict attention to equilateral n-gons such questions become quite challenging, even numerically: current algorithms for sampling equilateral n-gons use a Markov process which "folds" polygons while preserving closure and edgelengths and are only expected to converge in O(n^3) time. The main point of this talk is that a much better sampling algorithm and indeed much better answers are available if we widen our view to the space of n-gons in three dimensional space of fixed total length (rather than with fixed edgelengths). I will describe a natural probability measure on n-gons of total length 2 which is pushed forward from the standard measure on the Stiefel manifold of 2-frames in complex n-space using methods from algebraic geometry. We can directly sample the Stiefel manifold in O(n) time, which gives us a fast, direct sampling algorithm for closed n-gons via the pushforward map. We can also explicitly compute the expected radius of gyration and expected total curvature and even recover some topological information. This talk describes joint work primarily with Jason Cantarella (University of Georgia) and Tetsuo Deguchi (Ochanomizu University).

Wednesday, March 20, 2013

Posted January 29, 2013

3:30 pm - 4:20 pm Lockett 233

Margaret Doig, Indiana University
Virtual Seminar: "Obstructing finite surgery"

Abstract: We will discuss using Heegaard Floer invariants towards a partial classification of Dehn surgery on knots $K$ in $S^3$ which give elliptic manifolds $Y$ other than the lens spaces, sometimes called emph{finite, non-cyclic surgeries}. Recent results using these techniques include: if $p<10$ and $K$ is hyperbolic, there are no such $Y$; for any fixed $p$, there are at most finitely many $Y$ given by any $p/q$-surgery; if $pleq4$, there is a unique $p/q$-surgery (up to orientation) that gives an elliptic manifold, other than a lens space (for $g=1$, this was previously proved by Ghiggini: the surgery is $+1$ on the right-handed trefoil, and the manifold is the Poincar'e homology sphere).

Wednesday, April 10, 2013

Posted April 8, 2013

3:30 pm - 4:20 pm Lockett 233

Sam Nelson, Claremont McKenna College
Virtual Seminar: "Rack and Birack Module Invariants"

Abstract: In 2002, Andruskiewitsch and Gra\~na defined an algebra $R[x]$
associated to a rack $X$ and used it to generalize rack homology. In recent
work we have extended the rack algebra to the cases of biracks and twisted
virtual biracks. In this talk we will see new invariants of knots and links
defined from modules over these algebras.

Wednesday, October 2, 2013

Posted October 1, 2013

3:30 pm - 4:20 pm Lockett 233

Juanita Pinzon-Caicedo, Indiana University
Traceless SU(2) representations of 2-stranded tangles

Abstract: Given a codimension 2 submanifold A⊂X define R(X,A) as the space of traceless SU(2) representations of π_1(X\A) modulo conjugation. For Y a 3-manifold and K⊂Y a knot, Kronheimer-Mrowka defined the Instanton Knot Homology of (Y,K) as the homology of a chain complex whose groups are generated by the elements of R(Y,K). In the talk we describe a method to determine R(S^3,K) whenever K is a torus or pretzel knot.

Wednesday, October 23, 2013

Posted October 9, 2013

3:30 pm - 4:20 pm Lockett 233

Susan Abernathy, Louisiana State University
Virtual Seminar: "The Kauffman bracket ideal for genus-1 tangles"

Abstract: A genus-1 tangle is a 1-manifold with two boundary components properly embedded in the solid torus. A genus-1 tangle G embeds in a link L if we can complete G to L via a 1-manifold in the complement of the solid torus containing G. A natural question to ask is: given a tangle G and a link L, how can we tell if G embeds in L? We define the Kauffman bracket ideal, which gives an obstruction to tangle embedding, and outline a method for computing a finite list of generators for this ideal. We also give an example of a genus-1 tangle with non-trivial Kauffman bracket ideal and discuss how the concept of partial closures relates to this ideal.

Wednesday, October 30, 2013

Posted April 3, 2013

3:30 pm - 4:20 pm Lockett 233

Peter Horn, Syracuse University
Virtual Seminar: "Computing higher-order Alexander polynomials of knots"

Abstract: The classical Alexander polynomial of a knot can be de ned in several ways, one of which is via covering spaces. Using higher covering spaces, Cochran defi ned the higher-order Alexander polynomials. It is known that the degree of the classical Alexander polynomial gives a lower bound for the genus of a knot, and so do the degrees of the higher-order Alexander polynomials. These higher-order bounds are known to be stronger than the classical bound for satellite knots, but little is known about low crossing knots. We will present an algorithm to compute the degree of the first higher-order Alexander polynomial of any knot, and we will discuss some interesting computations.

Wednesday, November 6, 2013

Posted August 29, 2013

3:30 pm - 4:30 pm Lockett 233

Ina Petkova, Rice University
Virtual Seminar: "Bordered Floer homology and decategorification"

Abstract: Bordered Floer homology is a TQFT-type generalization of Heegaard Floer homology to 3-manifolds with boundary, which satisfies a nice gluing formula. I will give a brief description of this generalized theory, and discuss some applications to topology. For example, bordered Floer homology categorifies the kernel of the homology map induced by the inclusion of the boundary into the 3-manifold.

Wednesday, November 20, 2013

Posted August 29, 2013

3:30 pm - 4:20 pm Lockett 233

Eamonn Tweedy, Department of Mathematics, Rice University

Abstract: Cochran and Gompf defined a notion of positivity for concordance classes of knots that simultaneously generalizes the usual notions of sliceness and positivity of knots. Their positivity essentially amounts to the knot being slice in a positive-definite simply-connected four manifold. I'll discuss an analogous property for links, describe a concrete characterization of positivity upto concordance, and give some obstructions to positivity.

Wednesday, March 19, 2014

Posted March 13, 2014

3:30 pm - 4:20 pm Lockett 233

Olga Plamenevskaya, SUNY Stony Brook
Virtual Topology Seminar: "Looking for flexibility in higher-dimensional contact manifolds"

Abstract: Contact manifolds are odd-dimensional cousins of symplectic manifolds; a contact structure on a smooth manifold is a hyperplane field given as a kernel of a "non-degenerate" 1-form. Locally, all contact structures look the same, but globally, a lot of interesting topological phenomena arise. By a classical result of Eliashberg, contact manifolds in dimension 3 come in two flavors: tight (rigid) and overtwisted (flexible). While the tight ones are quite subtle, overtwisted contact structures are completely described by their algebraic topology. In higher dimensions, a class of flexible contact structures is yet to be found. We will describe some conjectural "overtwisted pieces" (due to Niederkruger et al.) and an important flexibility principle for certain Legendrian knots discovered by Murphy. Then, we will present some results (joint with E. Murphy, K. Niederkruger, and A. Stipsicz) showing that in the presence of an "overtwisted piece", all Legendrian knots are "flexible", and demonstrating some flexibility phenomena for contact manifolds in higher dimensions.

Wednesday, March 26, 2014

Posted March 14, 2014

3:30 pm - 4:30 pm Lockett 233

Equivariant Littlewood-Richardson coefficients

ABSTRACT. The goal of my talk (based on joint work with Edward Richmond) is to compute all equivariant Littlewood-Richardson (LR) coefficients for semisimple and Kac-Moody groups G, that is, the structure constants of the equivariant cohomology algebra H_B(G/B), where B is the Borel subgroup of G. These coefficients are of importance in enumerative geometry, algebraic combinatorics and representation theory. Our formula for the LR coefficients is purely combinatorial and is given in terms of the Cartan matrix and the Weyl group of G. In particular, our formula gives a combinatorial proof of positivity of the equivariant LR coefficients in the cases when all off-diagonal Cartan matrix entries are less than or equal to -2.

Wednesday, April 2, 2014

Posted March 30, 2014

3:30 pm - 4:30 pm Lockett 233

Chris Cornwell, Duke University
Virtual Seminar: Knot contact homology, knot group representations, and the A-polynomial

Abstract: In the knot contact homology of a knot K there are augmentations that may be associated to a flat connection on the complement of K. We show that all augmentations arise this way. As a consequence, a polynomial invariant of K called the augmentation polynomial represents a generalization of the classical A-polynomial. A recent conjecture, similar to the AJ conjecture concerning the A-polynomial, relates a 3-variable augmentation polynomial to colored HOMFLY-PT polynomials. Our results can be seen as motivation for this conjecture having an augmentation polynomial in place of the A-polynomial.

Wednesday, April 23, 2014

Posted April 21, 2014

3:30 pm - 4:20 pm Lockett 233

Mustafa Hajij, Department of Mathematics, LSU Graduate Student
Virtual Topology Seminar: " Skein Theory and q-Series"

Abstract: We study the tail a q-power series invariant of a sequence of admissible trivalent graphs with edges colored n or 2n. We use local skein relations to understand and compute the tail of these graphs. This allows us to understand the tail of the colored Jones polynomial for a large class of knots and links. For many quantum spin networks they turn out to be interesting number-theoretic q-series. In particular, certain quantum spin networks give a skein theoretic proof for the Andrews-Gordon identities for the two variable Ramanujan theta function as well to corresponding identities for the false theta function. Finally, we give product formula that the tail of such graphs satisfies.

Wednesday, September 17, 2014

Posted August 12, 2014

3:30 pm - 4:20 pm Lockett 233

Kristen Hendriks, UCLA
Virtual Seminar: "Localization and the link Floer homology of doubly-periodic knots"

Abstract: A knot K in S^3 is said to be q-periodic if there is an orientation-preserving action of Z_q on S^3 which preseves K and has fixed set an unknot disjoint from K. There are many classical obstructions to the possible periods of a knot, including Edmonds' condition on the genus and Murasugi's conditions on the Alexander polynomial. We construct localization spectral sequences on the link Floer homology of 2-periodic knots, and show that they give a simultaneous generalization of Edmonds' condition and one of Murasugi's conditions. We conclude with an example in which our spectral sequences give a stronger obstruction than these (although not all) classical conditions.

Wednesday, September 24, 2014

Posted September 22, 2014

3:30 pm - 4:20 pm 233 Lockett Hall

Robert Lipshitz, Columbia University
Virtual Seminar: "A Khovanov stable homotopy type"

Abstract: Khovanov homology is a knot invariant which refines (categorifies) the Jones polynomial. After recalling the definition of Khovanov homology we will introduce a space-level version, and sketch some computations and (modest) applications. This is joint work with Sucharit Sarkar and Tyler Lawson.

Wednesday, October 22, 2014

Posted October 7, 2014

3:30 pm - 4:20 pm Lockett 233

James Conway, Georgia Tech
Virtual Seminar: "Transverse Surgery in Contact 3-Manifolds"

Abstract: Much ink has been spilled on surgery on Legendrian knots; much less well studied is surgery on transverse knots. We will investigate transverse surgery, and study its effect on open books, the Heegaard Floer contact invariant, and tightness. We show that surgery on the connected binding of a genus g open book that supports a tight contact structure preserves tightness if the surgery coefficient is greater than 2g-1. In a complementary direction, we give criteria for when positive contact surgery on Legendrian knots will result in an overtwisted manifold.

Wednesday, February 4, 2015

Posted February 2, 2015

3:30 pm - 4:20 pm 233 Lockett Hall

Emily Stark, Tufts University
Abstract commensurability and quasi-isometric classification in dimension two

Two foundational questions in geometric group theory are to characterize the abstract commensurability and quasi-isometry classes within a class of groups, and to understand for which classes of groups the classifications coincide. In this talk, I will present a solution within the class of groups isomorphic to the fundamental group of two closed hyperbolic surfaces identified along an essential simple closed curve in each. I will discuss current work, joint with Pallavi Dani and Anne Thomas, for right-angled Coxeter groups.

Wednesday, March 18, 2015

Posted March 3, 2015

3:30 pm - 4:20 pm

Jeremy Van Horn-Morris, University of Arkansas
Virtual Seminar: On the coarse classification of Stein fillings

Abstract: In the '90s, Donaldson showed that every symplectic 4-manifold can be equipped with the structure of a Lefschetz pencil, a kind of singular surface bundle over CP^1. This pencil can be (non-uniquely) encoded as a relation in the mapping class group of a punctured surface, and while this factorization completely determines the manifold, it is in general very complicated. One might hope that some simpler shadow of the pencil might give useful information about the topology of the symplectic manifold. For example, what information does the genus of the pencil tell you about the symplectic manifold? Many of the initial conjectures about this relationship, as well as its generalization to open book decompositions, have been shown to be false. But, it turns out that in certain cases, there is very useful information available. We'll discuss the examples and the constraints. This is joint work with Inanc Baykur and Naoyuki Monden.

Wednesday, April 22, 2015

Posted October 7, 2014

3:30 pm - 4:20 pm tba

Tullia Dymarz, University of Wisconsin, Madison
Virtual Seminar: Non-rectifiable Delone sets in amenable groups

Abstract: In 1998 Burago-Kleiner and McMullen constructed the first examples of coarsely dense and uniformly discrete subsets of R^n that are not biLipschitz equivalent to the standard lattice Z^n. Similarly we find subsets inside the three dimensional solvable Lie group SOL that are not bilipschitz equivalent to any lattice in SOL. The techniques involve combining ideas from Burago-Kleiner with quasi-isometric rigidity results from geometric group theory.

Wednesday, September 16, 2015

Posted June 3, 2015

3:30 pm - 4:30 pm Lockett 233

Virtual Seminar: A transverse invariant from annular Khovanov homology

Abstract: Annular Khovanov homology is a refinement of Khovanov homology for links embedded in an annulus. Braid closures are natural examples of such links, and there is a well-known correspondence between braids and transverse links. Expanding on work of Plamenevskaya, I will present a computable conjugacy class invariant whose minimum we hope to be an effective transverse invariant. The invariant has applications to the word problem, the lengths of certain spectral sequences, and some classical questions about braids. This is joint work with Diana Hubbard.

Wednesday, October 21, 2015

Posted October 19, 2015

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

Virtual Seminar: Recent results concerning bridge spectra

Abstract: The bridge spectrum of a knot is a generalization of the classic invariant defined by Schubert, the bridge number of a knot. We will introduce the relevant background and some known results. Then we will give a short sketch of a proof of our main result, and end with open questions.

Wednesday, November 4, 2015

Posted June 17, 2015

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

Virtual Seminar: "The Symplectic Geometry of Polygon Space and How to Use It"

Abstract: In statistical physics, the basic (and highly idealized) model of a ring polymer is a closed random walk in 3-space with equal-length steps, often called a random equilateral polygon. In this talk, I will describe the moduli space of random equilateral polygons, giving a sense of how this fits into a larger symplectic and algebraic geometric story. In particular, the space of equilateral n-gons turns out to be a toric symplectic manifold, yielding a (nearly) global coordinate system. These coordinates are powerful tools both for proving theorems and for developing numerical techniques, some of which I will describe, including a very fast algorithm for directly sampling random polygons recently developed with Jason Cantarella (University of Georgia), Bertrand Duplantier (CEA/Saclay), and Erica Uehara (Ochanomizu University).

Wednesday, December 2, 2015

Posted September 24, 2015

3:30 pm - 4:30 pm

Chris Hruska, UW Milwaukee
Virtual Seminar: Distortion of surfaces in 3-dimensional graph manifolds

Abstract: (Joint with Hoang Thanh Nguyen) In geometric group theory, one often studies a finitely generated group as a geometric object, by equipping the group with a word metric. Using the word metric, Milnor observed that the fundamental group of any compact manifold closely resembles the universal cover of the manifold. If H is a finitely generated subgroup of G, then the inclusion of H into G may distort the geometry of H. In other words, distances between elements of H may be quite different when measured in the metrics of G and of H. We examine the large scale geometry of immersed horizontal surfaces in 3-dimensional graph manifolds. An immersed surface in a 3-manifold is said to be virtually embedded if the immersion lifts to an embedding into a finite sheeted cover of the manifold. We prove that the distortion of a horizontal surface is quadratic if the surface is virtually embedded, and is exponential otherwise. The proof depends on a combinatorial characterization of horizontal surfaces that virtually embed, due to Rubinstein-Wang. I will not assume any familiarity with geometric group theory or 3-dimensional manifolds in this talk.

Wednesday, February 17, 2016

Posted January 7, 2016

3:30 pm - 4:20 pm

Abhijit Champanerkar, CSI NY/CUNY
Virtual Seminar: "Densities and semi-regular tilings"

Abstract: For a hyperbolic knot or link $K$ the volume density is a ratio of hyperbolic volume to crossing number, and the determinant density is the ratio of 2pilog(det(K)) to the crossing number. We explore limit points of both densities for families of links approaching semi-regular biperiodic alternating links. We explicitly realize and relate the limits for both using techniques from geometry, topology, graph theory, dimer models, and Mahler measure of two-variable polynomials. This is joint work with Ilya Kofman and Jessica Purcell.

Wednesday, March 2, 2016

Posted November 21, 2015

3:30 pm - 4:20 pm 233 Lockett

Max Forester, University of Oklahoma
Virtual Seminar: "The geometry of Stallings-Bieri groups"

Abstract: The Stallings-Bieri groups are a family of finitely presented groups that have exotic homological finiteness properties, while also being quite easy to define and describe. They occur naturally as subgroups of non-positively curved groups (products of free groups, in fact). They are not non-positively curved themselves, however, and their large-scale geometry is quite interesting. I will discuss recent work with Will Carter in which we determine the large-scale isoperimetric behavior of these groups.

Wednesday, March 16, 2016

Posted March 9, 2016

3:30 pm - 4:20 pm

Roland van der Veen, Universiteit Leiden
Virtual Seminar: "Shadows, spines and gluing equations"

Abstract: Ideal triangulations were applied very effectively to understand 3-manifolds.
For example Thurston set up a system of gluing equations to produce hyperbolic structures
from the ideal triangulation. I will argue that their dual 2-complexes, known as spines, are both easier to visualize and more flexible than ideal triangulations. We will reformulate Thurston's construction in terms of spines and show how one proves their symplectic properties first found by Neumann and Zagier. Time permitting we will also mention relations to four-manifolds and the Andrews-Curtis conjecture that become apparent in terms of spines.

Wednesday, October 5, 2016

Posted September 22, 2016

3:30 pm - 4:20 pm Lockett 233

Fang Sun, Tulane University
Topological Symmetries of R^3

The absence of geometric rigidity regarding topological actions of finite group on R^3 drives us into looking for possible algebraic rigidity. The outcome is positive: If a finite group G acts topologically and faithfully on R^3, then G is isomorphic to a subgroup of O(3).

Wednesday, October 19, 2016

Posted September 22, 2016

3:30 pm - 4:20 pm Lockett 233

Rafal Komendarczyk, Tulane University
Ropelength, crossing number and finite-type invariants

Ropelength and embedding thickness are related measures of geometric complexity of classical knots and links in Euclidean space. In their recent work, Freedman and Krushkal posed a question regarding lower bounds for embedding thickness of n-component links in terms of Milnor linking numbers (mu-invariants). In this talk we will show how to obtain such estimates, generalizing the known linking number bound. In the process, we generalize the results of Kravchenko and Polyak on the arrow polynomial formulas of mu-invariants of string links. We also collect several facts about finite type invariants and ropelength/crossing number of knots giving examples of families of knots, where estimates via the finite type invariants outperform the well-known knot--genus estimate. This is joint work with Andreas Michaelides.

Wednesday, January 11, 2017

Posted November 1, 2016

3:30 pm Lockett 233

Sam Nelson, Claremont McKenna College
Biquasiles and Dual Graph Diagrams

Dual graph diagrams are an alternate way to present oriented knots and links in R^3. In this talk we will see how to turn dual graph Reidemeister moves into an algebraic structure known as biquasiles and use this structure to define new integer-valued counting invariants of oriented knots and links.

Wednesday, March 22, 2017

Posted February 27, 2017

3:30 pm - 4:20 pm Lockett 233

Christine Lee, University of Texas at Austin
Jones slopes and Murasugi sums of links

Abstract: A Jones surface for a knot in the three-sphere is an essential surface whose boundary slopes, Euler characteristic, and number of sheets correspond to quantities defined from the asymptotics of the degrees of colored Jones polynomial. The Strong Slope Conjecture by Garoufalidis and Kalfagianni-Tran predicts that there are Jones surfaces for every knot.

A link diagram D is said to be a Murasugi sum of two links D' and D'' if a state graph of D has a cut vertex, which separates the graph into two state graphs of D' and D'', respectively. We may obtain a state surface in the complement of the link K represented by D by gluing the state surface for D and the state surface for D' along the disk filling the circle represented by the cut vertex in the state graph. The resulting surface is called the Murasugi sum of the two state surfaces.

We consider near-adequate links which are certain Murasugi sums of near-alternating link diagrams with an adequate link diagram along their all-A state graphs with an additional graphical constraint. For a near-adequate knot, the Murasugi sum of the corresponding state surface is a Jones surface by the work of Ozawa. We discuss how this proves the Strong Slope Conjecture for this class of knots and we will also discuss the stability properties of their colored Jones polynomial.

Wednesday, April 5, 2017

Posted March 8, 2017

3:30 pm - 4:20 pm Lockett 233

Gregor Masbaum, CNRS, Institut de Mathematiques de Jussieu, Paris, France
An application of TQFT to modular representation theory

Wednesday, April 26, 2017

Posted February 3, 2017

3:30 pm - 4:20 pm Lockett 233

Jose Ceniceros, Louisiana State University
TBD

Wednesday, September 6, 2017

Posted August 14, 2017

3:30 pm - 4:30 pm Lockett 233

Peter Lambert-Cole, Georgia Institute of Technology
Conway mutation and knot Floer homology

Abstract: Mutant knots are notoriously hard to distinguish. Many, but not all, knot invariants take the same value on mutant pairs. Khovanov homology with coefficients in Z/2Z is known to be mutation-invariant, while the bigraded knot Floer homology groups can distinguish mutants such as the famous Kinoshita-Terasaka and Conway pair. However, Baldwin and Levine conjectured that delta-graded knot Floer homology, a singly-graded reduction of the full invariant, is preserved by mutation. In this talk, I will give a new proof that Khovanov homology mod 2 is mutation-invariant. The same strategy can be applied to delta-graded knot Floer homology and proves the Baldwin-Levine conjecture for mutations on a large class of tangles.

Wednesday, September 13, 2017

Posted August 24, 2017

3:30 pm - 4:30 pm Lockett 233

Mike Wong, Louisiana State University
An unoriented skein exact triangle for grid homology

Abstract: Like the Jones and Alexander polynomials, Khovanov and knot Floer homology (HFK) both satisfy an oriented and an unoriented skein exact triangle. Manolescu (2007) proved the unoriented triangle for HFK over Z/2Z. In this talk, we will give a combinatorial proof of the same using grid homology (GH), which is isomorphic to knot Floer homology. This gives rise to a cube-of-resolutions complex that calculates GH-tilde. If time permits, we will outline the generalisation to the case over Z, and an application to quasi-alternating links. No prior experience with the subject is needed, as a brief introduction to grid homology will be given.

Wednesday, September 27, 2017

Posted August 24, 2017

3:30 pm - 4:30 pm Lockett 233

John Etnyre, Georgia Institute of Technology
Contact surgeries and symplectic fillings

Abstract: It is well known that all contact manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. What is not so well understood is what properties of a contact structure are preserved by positive contact surgeries (the case for negative contact surgeries is fairly well understood now). In this talk we will discuss some new results about positive contact surgeries and in particular completely characterize when contact r surgery is symplectically fillable when r is in (0,1].

Wednesday, October 4, 2017

Posted August 24, 2017

3:30 pm - 4:30 pm Lockett 233

Mike Wong, Louisiana State University
TBD

Wednesday, October 18, 2017

Posted August 27, 2017

3:30 pm - 4:30 pm Lockett 233

Robin Koytcheff, University of Louisiana, Lafayette
Homotopy string links, configuration spaces, and the kappa invariant

Abstract: A link is an embedding of disjoint circles in space. A link homotopy is a path between two links where distinct components may not pass through each other, but where a component may pass through itself. In the 1990s, Koschorke conjectured that link homotopy classes of n-component links are distinguished by the kappa invariant. This invariant is essentially the map that a link induces on configuration spaces of n points. In joint work with F. Cohen, Komendarczyk, and Shonkwiler, we proved an analogue of this conjecture for string links. A key ingredient is a multiplication on maps of configuration spaces, akin to concatenation of loops in a space. This approach is related to recent joint work with Budney, Conant, and Sinha on finite-type knot invariants and the Taylor tower for the space of knots.

Wednesday, October 25, 2017

Posted September 13, 2017

3:30 pm - 4:30 pm Lockett 233

Yilong Wang, The Ohio State University
Integrality for SO(p)_2-TQFTs

Abstract: Representation theory of quantum groups at roots of unity give rise to modular tensor categories hence TQFTs, and the 3-manifold invariants from such constructions are known to be algebraic integers. In this talk, I will introduce the SO(p)_2-TQFT as an example of the above construction, and I will present our results on the integral lattices of the SO(p)_2-TQFT in genus 1 and one-punctured torus.

Wednesday, November 8, 2017

Posted November 7, 2017

3:30 pm - 4:30 pm Lockett 233

Mike Wong, Louisiana State University
Ends of moduli spaces in bordered Floer homology I

Abstract: Bordered Floer homology is an invariant associated to 3-manifolds with parametrized boundary, created by Lipshitz, Ozsvath, and Thurston as an extension of Heegaard Floer homology. In this framework, we associate a differential graded algebra A(F) to each surface, and an A-infinity module CF^(Y) to each bordered 3-manifold Y. The module CF^(Y) satisfies a structural equation that should be thought of as the analogue of the condition d^2=0 for chain complexes, obtained by considering ends of moduli spaces that appear in the definition of CF^(Y). In two consecutive expository talks, we will discuss specific examples that illustrate how these ends of moduli spaces match up in pairs. As a starting point, in this talk, we will first focus on the case of grid homology, a specialization of Heegaard Floer homology. No prior knowledge is necessary, as a brief introduction to grid homology will be given.

Wednesday, November 15, 2017

Posted November 15, 2017

3:30 pm - 4:30 pm Lockett 233

Mike Wong, Louisiana State University
Ends of moduli spaces in bordered Floer homology II

Abstract: This is the second in two consecutive talks about the ends of moduli spaces in Bordered Floer homology. Bordered Floer homology is an invariant associated to 3-manifolds with parametrized boundary, created by Lipshitz, Ozsvath, and Thurston as an extension of Heegaard Floer homology. In this framework, we associate a differential graded algebra A(F) to each surface, and an A-infinity module CF^(Y) to each bordered 3-manifold Y. The module CF^(Y) satisfies a structural equation that should be thought of as the analogue of the condition d^2=0 for chain complexes, obtained by considering ends of moduli spaces that appear in the definition of CF^(Y). In the talk last week, we discussed how these ends of moduli spaces match up in pairs in grid homology. In this talk, we will focus on the situation in bordered Floer homology, for both type A and type D structures.

Wednesday, February 21, 2018

Posted January 30, 2018

3:30 pm - 4:30 pm Lockett 233

Shea Vela-Vick, Louisiana State University
Knot Floer homology and fibered knots

Abstract: We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include a new proof that L-space knots prime and a classification of knots 3-manifolds with rank 3 knot Floer homology. We will also discuss a numerical refinement of the Ozsvath-Szabo contact invariant. This is joint work with John Baldwin.

Wednesday, February 28, 2018

Posted November 13, 2017

3:30 pm - 4:30 pm Lockett 233

Coarse geometry of right-angled Coxeter groups

Abstract: A main goal of geometric group theory is to understand finitely generated groups up to a coarse equivalence (quasi-isometry) of their Cayley graphs. Right-angled Coxeter groups (RACGs for short), in particular, are important classical objects that have been unexpectedly linked to the theory of hyperbolic 3-manifolds through recent results, including those of Agol and Wise. I will give a background on the relevant geometric group theory, RACGs and what is currently known regarding the quasi-isometric classification of RACGs. I will then describe a new computable quasi-isometry invariant, the hypergraph index, and its relation to other invariants such as divergence and thickness.

Wednesday, March 7, 2018

Posted October 18, 2017

3:30 pm - 4:30 pm Lockett 233

Bulent Tosun, University of Alabama
Obstructing Stein structures on contractible 4-manifolds

Abstract: A Stein manifold is a complex manifold with particularly nice convexity properties. In real dimensions above 4, existence of a Stein structure is essentially a homotopical question, but for 4-manifolds the situation is more subtle. An important question that has been circulating among contact and symplectic topologist for some time asks: whether every contractible smooth 4-manifold admits a Stein structure? In this talk we will provide examples that answer this question negatively. Moreover, along the way we will provide new evidence to a closely related fascinating conjecture of Gompf, which asserts that a nontrivial Brieskorn homology sphere, with either orientation, cannot be embedded in complex 2-space as the boundary of a Stein submanifold. This is a joint work with Tom Mark.

Wednesday, March 14, 2018

Posted October 18, 2017

3:30 pm - 4:30 pm

Ina Petkova, Dartmouth College
Knot Floer homology and the gl(1|1) link invariant

Abstract: The Reshetikhin-Turaev construction for the standard representation of the quantum group gl(1|1) sends tangles to C(q)-linear maps in such a way that a knot is sent to its Alexander polynomial. After a brief review of this construction, I will give an introduction to tangle Floer homology - a combinatorial generalization of knot Floer homology which sends tangles to (homotopy equivalence classes of) bigraded dg bimodules. Finally, I will discuss how to see tangle Floer homology as a categorification of the Reshetikhin-Turaev invariant. This is joint work with Alexander Ellis and Vera Vertesi.

Wednesday, March 21, 2018

Posted January 10, 2018

3:30 pm - 4:30 pm Lockett 233

Piecewise-linear disks and spheres in 4-manifolds

Abstract: We discuss a variety of problems related to the existence of piecewise-linear (PL) embedded surfaces in smooth 4-manifolds. We give the first known example of a smooth, compact 4-manifold which is homotopy equivalent to the 2-sphere but for which the homotopy equivalence cannot be realized by a PL embedding. We also show that the PL concordance group of knots in homology 3-spheres is infinitely generated and contains elements of infinite order. This is joint work with Jen Hom and Tye Lidman.

Wednesday, April 25, 2018

Posted November 12, 2017