LSU Virtual Topology Seminar
Fall 2018–Spring 2019

Organizers: Shea Vela-Vick, Mike Wong
Last updated: Nov 6, 2018

Previous year: Fall 2017–Spring 2018

Time and venueThe LSU Virtual Topology Seminar meets in 233 Lockett Hall, at 3:30 pm CT on Wednesdays.

BroadcastingResearchers from other institutions are welcome to participate in the virtual seminar, which is broadcast online using Viewme, a video collaboration program. If you are interested in joining us, please send an e-mail to cmmwong [at] lsu [dot] edu.

Mailing list If you would like to (un)subscribe to the mailing list, please send an e-mail to shea [at] math [dot] lsu [dot] edu.

Schedule The schedule is updated throughout the academic year, and only confirmed speakers are listed below.
Date Speaker Institution Title
Aug 29, 2018 Ignat Soroko Louisiana State University Dehn functions of subgroups of right-angled Artin groups
Sep 5, 2018 Andrew Zimmer Louisiana State University Limit sets of discrete subgroups
Sep 26, 2018 Yilong Wang Louisiana State University Modular tensor categories and Reshetikhin–Turaev TQFTs I
Oct 10, 2018 Yilong Wang Louisiana State University Modular tensor categories and Reshetikhin–Turaev TQFTs II
Oct 17, 2018 Joshua Sabloff Haverford College Length and width of Lagrangian cobordisms
Oct 24, 2018 Scott Baldridge Louisiana State University A new cohomology for planar trivalent graphs with perfect matchings
Oct 31, 2018 Matthew Haulmark Vanderbilt University Non-hyperbolic groups with Menger curve boundary
Nov 7, 2018 Andrew McCullough Georgia Institute of Technology Legendrian large cables and non-uniformly thick knots
Nov 14, 2018 Marco Marengon UCLA Strands algebras and Ozsváth–Szabó’s Kauffman states functor
Jan 9, 2019 Genevieve Walsh Tufts University TBA
Jan 30, 2019 Francesco Lin Princeton University TBA
Feb 6, 2019 Caitlin Leverson Georgia Institute of Technology TBA
Mar 27, 2019 Tye Lidman North Carolina State University TBA

Abstracts


Date Aug 29, 2018

Speaker Ignat Soroko

Title Dehn functions of subgroups of right-angled Artin groups

Abstract The question of what is a possible range for the Dehn functions (a.k.a. isoperimetric profile) for certain classes of groups is a natural and interesting one. Due to works of many authors starting with Gromov, we know a lot about the isoperimetric profile for the class of all finitely presented groups. Much less is known for many natural subclasses of groups, such as subgroups of right-angled Artin groups. We prove that polynomials of arbitrary degree are realizable as Dehn functions of subgroups of right-angled Artin groups. The key step is to construct for each natural k a free-by-cyclic group with the monodromy automorphism growing as n^k, which is virtually special in the sense of Haglund and Wise. Then its double will have Dehn function growing as n^{k+2}. This is a joint work with Noel Brady.

Date Sep 5, 2018

Speaker Andrew Zimmer

Title Limit sets of discrete subgroups

Abstract Given a discrete group of matrices one can define an associated limit set in projective space. In this talk I'll describe some results concerning the regularity of this limit set when the discrete group satisfies certain geometric properties.

Date Sep 26, 2018

Speaker Yilong Wang

Title Modular tensor categories and Reshetikhin–Turaev TQFTs I

Abstract In this talk, we give a detailed introduction to modular tensor categories and the Reshetikhin–Turaev TQFT associated to them. Time permitted, I will talk about algebraic properties of the RT-TQFTs.

Date Oct 10, 2018

Speaker Yilong Wang

Title Modular tensor categories and Reshetikhin–Turaev TQFTs II

Abstract In this talk, I will define ribbon and modular categories, and show how modular categories give rise to representations of the modular group SL(2,Z) using the graphical calculus introduced last time. Time permitted, I will explain how to generalize the construction to obtain a TQFT for closed surfaces.

Date Oct 17, 2018

Speaker Joshua Sabloff

Title Length and width of Lagrangian cobordisms

Abstract In this talk, I will discuss two measurements of Lagrangian cobordisms between Legendrian submanifolds in symplectizations: their length and their relative Gromov width. The Gromov width, in particular, is a fundamental global invariant of symplectic manifolds, and a relative version of that width helps understand the geometry of Lagrangian submanifolds of a symplectic manifold. Lower bounds on both the length and the width may be produced by explicit constructions; this talk will concentrate on upper bounds that arise from a filtered version of Legendrian contact homology, a Floer-type invariant. This is joint work with Lisa Traynor.

Date Oct 24, 2018

Speaker Scott Baldridge

Title A new cohomology for planar trivalent graphs with perfect matchings

Abstract In this lecture, I will describe a simple-to-compute polynomial invariant of a planar trivalent graph with a perfect matching (think: Jones polynomial for graphs). This polynomial is interesting because of what it detects: If the polynomial is non-zero when evaluated at one, then the perfect matching is even. Such a perfect matching implies that the graph can be 4-colored. I will then show how to categorify this polynomial to get a Khovanov-like cohomology theory for planar trivalent graphs and compute a couple of simple examples. If time permits, I will talk about some consequences of the cohomology theory.

Date Oct 31, 2018

Speaker Matthew Haulmark

Title Non-hyperbolic groups with Menger curve boundary

Abstract In the setting of hyperbolic groups, groups with Menger curve boundary are known to be abundant. Given the prevalence of negatively curved groups, it was a surprising observation of Ruane that there were no known examples of non-hyperbolic groups with Menger curve boundary found in the literature. Thus Ruane posed the problem (early 2000s) of finding examples (alt. interesting classes) of non-hyperbolic groups with Menger curve boundary. In this talk I will discuss the first class of such examples. This is joint work with Chris Hruska and Bakul Sathaye.

Date Nov 7, 2018

Speaker Andrew McCullough

Title Legendrian large cables and non-uniformly thick knots

Abstract We will define the notion of a knot type having Legendrian large cables, and discuss the fact that having this property implies that the knot type is not uniformly thick. In this case, there are solid tori in this knot type that do not thicken to a solid torus with integer slope boundary torus, and that exhibit new phenomena; specifically, they have virtually overtwisted contact structures. We will give an example of an infinite family of ribbon knots that have Legendrian large cables which fail to be uniformly thick in several ways not previously seen.

Date Nov 14, 2018

Speaker Marco Marengon

Title Strands algebras and Ozsváth–Szabó’s Kauffman states functor

Abstract Ozsváth and Szabó introduced in 2016 a knot invariant, which they announced to be isomorphic to the usual knot Floer homology. Their construction is reminiscent of bordered Floer homology: for example, their invariant is defined by tensoring bimodules over certain algebras. During the talk I will introduce a more geometric construction, closer in spirit to bordered sutured Floer homology, based on strands on a particular class of generalised arc diagrams. The resulting strands algebras are quasi-isomorphic to the Ozsváth–Szabó algebras, suggesting that Ozsváth and Szabó’s theory may be part of a hypothetical generalisation of bordered sutured Floer homology. This is a joint work with Mike Willis and Andy Manion.

Date Jan 9, 2019

Speaker Genevieve Walsh

Title TBA

Abstract TBA

Date Jan 30, 2019

Speaker Francesco Lin

Title TBA

Abstract TBA

Date Feb 6, 2019

Speaker Caitlin Leverson

Title TBA

Abstract TBA

Date Mar 27, 2019

Speaker Tye Lidman

Title TBA

Abstract TBA