Topology Seminar
Seminar website

Posted October 1, 2003

3:30 pm - 4:30 pm Lockett 243
Patrick Gilmer, Mathematics Department, LSU

Integrality for TQFTs

Topology Seminar
Seminar website

Posted October 21, 2003

3:30 pm - 4:30 pm Lockett 243
Richard A. Litherland, Mathematics Department, LSU

On the Ozsvath-Szabo homology theory

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted January 27, 2004

Last modified January 30, 2004

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

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted March 3, 2004

Last modified March 12, 2004

Neal Stoltzfus, Mathematics Department, LSU

Diagonalization of the Lickorish Form on Non-crossing Chord Diagrams

Topology Seminar
Seminar website

Posted March 22, 2004

Last modified March 25, 2004

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

Topology Seminar
Seminar website

Posted September 8, 2004

4:10 pm - 5:00 pm Lockett 284
Scott Baldridge, LSU

Introduction to 4-Manifold Theory, I

Topology Seminar
Seminar website

Posted September 20, 2004

4:10 pm - 5:00 pm Lockett 284
Scott Baldridge, LSU

Introduction to 4-manifold theory, II

Topology Seminar
Seminar website

Posted September 21, 2004

4:10 pm - 5:00 pm Lockett 284
Scott Baldridge, LSU

Introduction to 4-Manifolds III

Topology Seminar
Seminar website

Posted September 24, 2004

Last modified October 1, 2004

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

Topology Seminar
Seminar website

Posted February 10, 2005

Last modified February 15, 2005

Daniel C. Cohen, Mathematics Department, LSU

Topology and Combinatorics of boundary manifolds of arrangements

Joint Virtual Seminar with the University of Iowa

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted March 1, 2005

Last modified March 7, 2005

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.

Topology Seminar
Seminar website

Posted March 9, 2005

Last modified March 11, 2005

Patrick Gilmer, Mathematics Department, LSU

Integral Lattices in TQFT

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted March 15, 2005

Last modified April 14, 2005

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

Topology Seminar
Seminar website

Posted April 6, 2005

Last modified April 19, 2005

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.

Topology Seminar
Seminar website

Posted April 19, 2005

3:30 pm - 4:30 pm Lockett 285
Ambar Sengupta, Mathematics Department, LSU

Quantum Physics from Pure Logic

Topology Seminar
Seminar website

Posted March 27, 2005

Last modified April 27, 2005

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.

Topology Seminar
Seminar website

Posted April 27, 2005

Last modified May 3, 2005

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.

Topology Seminar
Seminar website

Posted August 16, 2005

Last modified September 6, 2005

Nathan Broaddus, Cornell University

Non-cyclic covers of knot complements

Topology Seminar
Seminar website

Posted September 8, 2005

Last modified September 13, 2005

Brendan Owens, LSU

Floer homology of double branched covers

Topology Seminar
Seminar website

Posted September 9, 2005

4:10 pm - 5:00 pm Lockett 285
Brendan Owens, LSU

Floer homology of double branched covers, Part II

Topology Seminar
Seminar website

Posted September 13, 2005

4:10 pm - 5:00 pm Lockett 285
Brendan Owens, LSU

Floer homology of double branched covers, Part III

Topology Seminar
Seminar website

Posted September 19, 2005

4:10 pm - 5:00 pm Lockett 285
Scott Baldridge, LSU

Symplectic 4-manifolds with prescribed fundamental group

Topology Seminar
Seminar website

Posted October 4, 2005

4:10 pm - 5:00 pm Lockett 285
Scott Baldridge, LSU

Symplectic 4-manifolds with prescribed fundamental group, Part II

Topology Seminar
Seminar website

Posted October 12, 2005

Last modified October 15, 2005

Tara Brendle, Department of Mathematics, LSU

The Birman-Craggs-Johnson homomorphism and the homology of the Johnson Kernel

Topology Seminar
Seminar website

Posted October 12, 2005

Last modified October 14, 2005

Tara Brendle, Department of Mathematics, LSU

The Birman-Craggs-Johnson homomorphism and the homology of the Johnson Kernel, Part II

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted November 14, 2005

4:10 pm - 5:00 pm Lockett 285
Khaled Qazaqzeh, LSU

Integral Bases for Certain TQFT-Modules of the Torus

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted January 24, 2006

Last modified January 26, 2006

Daniel C. Cohen, Mathematics Department, LSU

tba

Topology Seminar
Seminar website

Posted January 26, 2006

Last modified February 1, 2006

Neal Stoltzfus, Mathematics Department, LSU

Root Posets and Temperley-Lieb Algebras

Topology Seminar
Seminar website

Posted February 8, 2006

4:40 pm - 5:30 pm Lockett 284
Ben McReynolds, UT Austin

Separable subgroups of mapping class groups

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted March 9, 2006

4:40 pm - 5:30 pm Lockett 284
Patrick Gilmer, Mathematics Department, LSU

Lollipop trees in TQFT

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted May 1, 2006

Last modified May 9, 2006

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

results about links with cyclotomic Jones polynomials.

Topology Seminar
Seminar website

Posted September 5, 2006

Last modified September 19, 2006

Patrick Gilmer, Mathematics Department, LSU

Surgery of type-p and quantum invariants of 3-manifolds

Topology Seminar
Seminar website

Posted September 6, 2006

Last modified September 19, 2006

Neal Stoltzfus, Mathematics Department, LSU

Dessins in Knot Theory

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted October 4, 2006

Last modified October 10, 2006

Indira Lara Chatterji, Ohio State University

A characterization of hyperbolicity.

Topology Seminar
Seminar website

Posted October 17, 2006

4:40 pm - 5:30 pm Lockett 284
Brendan Owens, LSU

Knot surgeries and negative definite four manifolds

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted November 3, 2006

Last modified November 8, 2006

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.

Topology Seminar
Seminar website

Posted January 10, 2007

Last modified January 21, 2007

Emille K. Davie, University of Georgia

Characterizing Right-Veering Surface Diffeomorphisms Via the Burau Representation

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted March 21, 2007

Last modified March 28, 2007

Stephen Bigelow, UC Santa Barbara

Representations of Planar Algebras

Time/Date Changed

Topology Seminar
Seminar website

Posted August 27, 2007

Last modified August 31, 2007

Adam Lowrance, Department of Mathematics, Vassar College

On Knot Floer Width and Turaev Genus

Topology Seminar
Seminar website

Posted September 5, 2007

4:30 pm - 5:30 pm Lockett 276
Steve Wallace, LSU

Surgery untying of knots

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted September 13, 2007

Last modified September 18, 2007

Neal Stoltzfus, Mathematics Department, LSU

Quasi-Trees and Khovanov homology

Virtual Seminar together with U Iowa

Topology Seminar
Seminar website

Posted September 19, 2007

4:40 pm - 5:30 pm Lockett 276
Scott Baldridge, LSU

A symplectically aspherical manifold with b_1=1

Topology Seminar
Seminar website

Posted September 24, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663
Adam Lowrance, Department of Mathematics, Vassar College

On knot Floer width and Turaev genus, Part I

Virtual Seminar together with U Iowa

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted September 24, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663
Adam Lowrance, Department of Mathematics, Vassar College

On knot Floer width and Turaev genus,Part II

Virtual Seminar together with U Iowa

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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)

Topology Seminar
Seminar website

Posted October 3, 2007

Last modified October 11, 2007

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

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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)

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted October 25, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663Jeff Boerner (U Iowa): On the Asaeda-Przytycki-Sikora homology

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

Topology Seminar
Seminar website

Posted October 25, 2007

Last modified October 30, 2007

Junior Topology Seminar

This is a reading seminar. See this announcement

Topology Seminar
Seminar website

Posted November 4, 2007

3:40 pm - 4:30 pm Biological Sciences Annex Building - A663Heather 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)

Topology Seminar
Seminar website

Posted November 6, 2007

12:40 pm - 1:30 pm Lockett 119Junior Topology Seminar

Reading seminar. See here

Topology Seminar
Seminar website

Posted November 6, 2007

4:40 pm - 5:30 pm Lockett 276
Patrick Gilmer, Mathematics Department, LSU

Congruence and quantum invariants

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted November 6, 2007

12:40 pm - 1:30 pm Lockett 119Junior Topology Seminar

Reading Seminar. See here

Topology Seminar
Seminar website

Posted November 6, 2007

3:40 pm - 4:30 pmNO VIRTUAL SEMINAR (THANKSGIVING)

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted January 22, 2008

Last modified January 28, 2008

Charles Frohman, University of Iowa

sl_3 Topological Quantum Field Theory after Khovanov

Virtual Seminar together with UIowa

Topology Seminar
Seminar website

Posted January 24, 2008

Last modified February 14, 2008

A diagramless link homology

Adam McDougall (Virtual Seminar together with UIowa)

Topology Seminar
Seminar website

Posted January 24, 2008

Last modified February 15, 2008

Hee Jung Kim, Department of Mathematics, LSU

Embeddings of Surfaces in 4-manifolds

(Virtual Seminar together with UIowa)

Topology Seminar
Seminar website

Posted January 30, 2008

Last modified February 25, 2008

Gregor Masbaum, University Paris 7

TQFT and the Nielsen-Thurston classification of surface homeomorphisms

Topology Seminar
Seminar website

Posted February 20, 2008

Last modified February 27, 2008

Alissa Crans, University of Chicago/Loyola Marymount University

2-groups: Categorified groups

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

Topology Seminar
Seminar website

Posted February 20, 2008

Last modified March 20, 2008

Hee Jung Kim, Department of Mathematics, LSU

Knotting Surfaces in 4-manifolds, Part II

(Virtual Seminar together with UIowa)

Topology Seminar
Seminar website

Posted January 24, 2008

Last modified March 31, 2008

Charles Livingston, Indiana University

Twisted Alexander polynomials, metabelian representations, and the knot slicing problem

Topology Seminar
Seminar website

Posted February 20, 2008

Last modified April 1, 2008

Models for evaluating the Homfly polynomial

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

Topology Seminar
Seminar website

Posted April 7, 2008

Last modified April 8, 2008

Cody Armond, Department of Mathematics, LSU

On the Huynh-Le Quantum Determinant for the Colored Jones Polynomial

(Virtual Seminar together with UIowa)

Topology Seminar
Seminar website

Posted February 18, 2008

Last modified April 4, 2008

Oleg Viro, SUNY Stony Brook

Twisted acyclicity of circle and link signatures

Topology Seminar
Seminar website

Posted February 27, 2008

Last modified April 21, 2008

Joan Birman, Columbia University/Barnard College
Receipient of the Chauvenet Prize

Twisted torus knots and Lorenz knots

Topology Seminar
Seminar website

Posted August 22, 2008

3:40 pm X-labTest run for Virtual Seminar

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

Topology Seminar
Seminar website

Posted September 10, 2008

3:30 pm - 4:30 pm X-lab: Lockett 233
Heather Russell, USC

Virtual Seminar

Live from Iowa City

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted October 1, 2008

3:40 pm - 4:30 pm X-lab: Lockett 233Virtual Seminar with UIowa/UMiami

Adam McDougall (U Iowa): On the diagramless link homology

Talk is broadcasted from Iowa

Topology Seminar
Seminar website

Posted October 1, 2008

3:40 pm - 4:30 pm X-lab: Lockett 233Virtual Seminar with UIowa/UMiami

Ken Baker (University of Miami)

(talk is broadcasted from Miami)

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

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

Topology Seminar
Seminar website

Posted February 10, 2009

3:40 pm - 4:40 pm Lockett 233
Chad Giusti, University of Oregon

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted March 11, 2010

Last modified March 22, 2010

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.

Topology Seminar
Seminar website

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)

Topology Seminar
Seminar website

Posted March 18, 2011

Last modified March 29, 2011

Kate Kearney, Indiana University

An Obstruction to Knots Bounding Moebius Bands

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted September 9, 2011

Last modified September 22, 2011

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.

Topology Seminar
Seminar website

Posted August 29, 2011

Last modified September 26, 2011

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted September 8, 2011

Last modified September 22, 2011

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).

Topology Seminar
Seminar website

Posted September 23, 2011

Last modified October 25, 2011

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted September 23, 2011

Last modified November 3, 2011

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.

Topology Seminar
Seminar website

Posted October 31, 2011

Last modified November 4, 2011

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)

Topology Seminar
Seminar website

Posted December 21, 2011

3:40 pm - 4:30 pm Lockett 233
Benjamin Himpel, Centre for Quantum Geometry of Moduli Spaces, Aarhus, Denmark

tba

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted January 28, 2012

Last modified January 31, 2012

Cody Armond, Department of Mathematics, LSU

"The colored Jones polynomial and adequate links"

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted February 26, 2012

Last modified March 14, 2012

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.

Topology Seminar
Seminar website

Posted March 7, 2012

Last modified March 14, 2012

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted April 3, 2012

Last modified May 8, 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.

Topology Seminar
Seminar website

Posted August 26, 2012

Last modified September 3, 2012

Anastasiia Tsvietkova, LSU

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.

Topology Seminar
Seminar website

Posted August 21, 2012

Last modified September 3, 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.

Topology Seminar
Seminar website

Posted September 1, 2012

Last modified September 14, 2012

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted September 14, 2012

Last modified October 16, 2012

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.

Topology Seminar
Seminar website

Posted September 19, 2012

Last modified October 23, 2012

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.

Topology Seminar
Seminar website

Posted December 3, 2012

Last modified January 22, 2013

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.

Topology Seminar
Seminar website

Posted December 3, 2012

Last modified January 25, 2013

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.

Topology Seminar
Seminar website

Posted December 3, 2012

Last modified January 28, 2013

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted January 22, 2013

Last modified March 5, 2013

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).

Topology Seminar
Seminar website

Posted January 29, 2013

Last modified March 21, 2013

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).

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted October 9, 2013

Last modified October 10, 2013

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.

Topology Seminar
Seminar website

Posted April 3, 2013

Last modified October 1, 2013

Peter Horn, Syracuse University

Virtual Seminar: "Computing higher-order Alexander polynomials of knots"

Abstract: The classical Alexander polynomial of a knot can be dened in several ways, one of which is via covering spaces. Using higher covering spaces, Cochran defined 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.

Topology Seminar
Seminar website

Posted August 29, 2013

Last modified November 5, 2013

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.

Topology Seminar
Seminar website

Posted August 29, 2013

Last modified November 14, 2013

Eamonn Tweedy, Department of Mathematics, Rice University

Virtual Seminar: "Positive Links"

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

Posted March 14, 2014

3:30 pm - 4:30 pm Lockett 233
Arkady Berenstein, University of Oregon

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

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.

Topology Seminar
Seminar website

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.

Topology Seminar
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Posted October 7, 2014

Last modified October 23, 2014

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.

Topology Seminar
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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.

Topology Seminar
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Posted March 3, 2015

Last modified March 16, 2015

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.

Topology Seminar
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Posted October 7, 2014

Last modified April 16, 2015

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.

Topology Seminar
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Posted June 3, 2015

Last modified September 9, 2015

Adam Saltz, Boston College

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.

Topology Seminar
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Posted October 19, 2015

3:30 pm - 4:30 pm 233 Lockett Hall
Nicholas Owad, University of Nebraska, Lincoln

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.

Topology Seminar
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Posted June 17, 2015

Last modified November 4, 2015

Clayton Shonkwiler, Colorado State University

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).

Topology Seminar
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Posted September 24, 2015

Last modified November 30, 2015

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.

Topology Seminar
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Posted January 7, 2016

Last modified February 8, 2016

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.

Topology Seminar
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Posted November 21, 2015

Last modified February 25, 2016

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.

Topology Seminar
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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.

Topology Seminar
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Posted September 22, 2016

Last modified October 5, 2016

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).

Topology Seminar
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Posted September 22, 2016

Last modified October 11, 2016

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.

Topology Seminar
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Posted November 1, 2016

Last modified January 3, 2017

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.

Topology Seminar
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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.

Topology Seminar
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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

Topology Seminar
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Posted February 3, 2017

3:30 pm - 4:20 pm Lockett 233
Jose Ceniceros, Louisiana State University

TBD

Topology Seminar
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Posted August 14, 2017

Last modified August 15, 2017

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.

Topology Seminar
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Posted August 24, 2017

Last modified September 12, 2017

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.

Topology Seminar
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Posted August 24, 2017

Last modified September 20, 2017

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].

Topology Seminar
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Posted August 24, 2017

Last modified September 19, 2017

Mike Wong, Louisiana State University

TBD

Topology Seminar
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Posted August 27, 2017

Last modified October 16, 2017

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.

Topology Seminar
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Posted September 13, 2017

Last modified September 20, 2017

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.

Topology Seminar
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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.

Topology Seminar
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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.

Topology Seminar
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Posted January 30, 2018

Last modified February 7, 2018

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.

Topology Seminar
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Posted November 13, 2017

Last modified February 26, 2018

Ivan Levcovitz, CUNY Graduate Center

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.

Topology Seminar
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Posted October 18, 2017

Last modified February 27, 2018

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.

Topology Seminar
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Posted October 18, 2017

Last modified March 13, 2018

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.

Topology Seminar
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Posted January 10, 2018

Last modified March 20, 2018

Adam Levine, Duke University

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.

Topology Seminar
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Posted November 12, 2017

Last modified April 22, 2018

Miriam Kuzbary, Rice University

Perspectives on Link Concordance Groups

Abstract: The knot concordance group has been the subject of much study since its introduction by Ralph Fox and John Milnor in 1966. One might hope to generalize the notion of a concordance group to links; however, the immediate generalization to the set of links up to concordance does not form a group since connected sum of links is not well-defined. In this talk, I will discuss two notions of a link concordance group: the string link concordance group due to Le Dimet in 1988 and one due to Matthew Hedden and myself based on the knotification construction of Peter Ozsvath and Zoltan Szabo. I will present invariants for studying these groups coming from Heegaard-Floer homology and a new group theoretic invariant for studying concordance of knots inside in certain types of 3-manifold, as well a preliminary result involving more classical link concordance invariants.