Talk_id  Date  Speaker  Title 
29397

Tuesday 9/6 3:00 PM

G&T Seminar, MSU

Organizational Meeting
 G&T Seminar, MSU
 Organizational Meeting
 09/06/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
Organizational meeting for the GT seminar this Fall.

29403

Tuesday 9/20 3:00 PM

Bin Sun, Oxford

$L^2$Betti numbers of fiber bundles
 Bin Sun, Oxford
 $L^2$Betti numbers of fiber bundles
 09/20/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
We study the $L^2$Betti numbers of fiber bundles $F \rightarrow E \rightarrow B$ of manifolds. Under certain conditions (e.g., when $F$ is simply connected), $b_*^{(2)}(E)$ can be computed using the twisted $L^2$Betti numbers of $B.$ We relate the twisted and untwisted $L^2$Betti numbers of $B$ when $\pi_1(B)$ is locally indicable. As an application, we compute $b_*^{(2)}(E)$ when $B$ is either a surface or a nonpositively curved $3$manifold. This is a joint work with Dawid Kielak.

30447

Tuesday 10/4 3:00 PM

Peter Johnson, Michigan State University

Knot lattice homology and the GukovManolescu 2variable series
 Peter Johnson, Michigan State University
 Knot lattice homology and the GukovManolescu 2variable series
 10/04/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Peter Kilgore Johnson (john8251@msu.edu)
In previous work of Akhmechet, Krushkal, and the speaker, a unification of lattice cohomology and the $\widehat{Z}$invariant was established. Both theories are combinatorially defined invariants of plumbed 3manifolds, but with quite different origins. Lattice cohomology, due to Némethi, is motivated by the study of normal surface singularities and is isomorphic to Heegaard Floer homology for plumbing trees. On the other hand, $\widehat{Z}$, due to GukovPeiPutrovVafa, is a power series coming from a physical theory and is conjectured to recover quantum invariants of 3manifolds at roots of unity. In this talk, I will discuss work in progress relating knot lattice homology and the GukovManolescu 2variable series, the knot theoretic counterparts to lattice homology and $\widehat{Z}$. This is joint work with Ross Akhmechet and Sunghyuk Park.

29432

Tuesday 10/11 3:00 PM

Daniel Douglas, Yale

Dimers, webs, and local systems
 Daniel Douglas, Yale
 Dimers, webs, and local systems
 10/11/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
For a planar bipartite graph G equipped with a SLnlocal system, we show that the determinant of the associated Kasteleyn matrix counts “nmultiwebs” (generalizations of nwebs) in G, weighted by their webtraces. We use this fact to study random nmultiwebs in graphs on some simple surfaces. Time permitting, we will discuss some relations to FockGoncharov theory. This is joint work with Rick Kenyon and Haolin Shi.

29418

Tuesday 10/18 3:00 PM

Juan MuñozEchániz, Columbia University

Families of contact structures and monopole Floer homology
 Juan MuñozEchániz, Columbia University
 Families of contact structures and monopole Floer homology
 10/18/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Peter Kilgore Johnson (john8251@msu.edu)
The contact invariant, defined by Kronheimer and Mrowka, is
an element in the monopole Floer homology of a 3manifold canonically
attached to a contact structure. I will discuss how the contact
invariant places constraints on the topology of families of contact
structures, and how it can be used to detect nontrivial
contactomorphisms given by "Dehn twists" on spheres. The main new tool
is a generalisation of the contact invariant to an invariant of
families of contact structures.

29433

Tuesday 11/1 3:00 PM

Ka Ho Wong, Texas A&M

On the 1loop conjecture of fundamental shadow link complements
 Ka Ho Wong, Texas A&M
 On the 1loop conjecture of fundamental shadow link complements
 11/01/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
The 1loop conjecture proposed by Dimofte and Garoufalidis suggests a simple and explicit formula to compute the adjoint twisted Reidemeister torsion of hyperbolic 3manifolds with toroidal boundary in terms of the shape parameters of any ideal triangulation of the manifolds. In this talk, I will give a brief overview of the conjecture and present our recent result on the 1loop conjecture for fundamental shadow link complements. This is a joint work with Tushar Pandey.

30477

Monday 11/7 2:00 PM

Calvin McPhailSnyder , Duke University

RTG Seminar: Quantum and hyperbolic invariants of knots (Introductory talk)
 Calvin McPhailSnyder , Duke University
 RTG Seminar: Quantum and hyperbolic invariants of knots (Introductory talk)
 11/07/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Efstratia Kalfagianni (kalfagia@msu.edu)
This talk consists of two related but distinct parts, and should be accessible if you know some algebraic topology and/or differential geometry. The first part is about quantum invariants: I will sketch how to compute the colored Jones polynomials of a knot and discuss their origin in representation theory. The second part is about hyperbolic geometry: I will discuss the basics of hyperbolic knot theory and explain how to compute hyperbolic structures and their volumes using ideal triangulations. The goal is to motivate the volume conjecture discussed in my main talk, which relates the colored Jones polynomials to the hyperbolic volume.

29411

Tuesday 11/8 3:00 PM

Calvin McPhailSnyder , Duke University

Hyperbolic tensor networks and the volume conjecture
 Calvin McPhailSnyder , Duke University
 Hyperbolic tensor networks and the volume conjecture
 11/08/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Efstratia Kalfagianni (kalfagia@msu.edu)
Quantum invariants of links like the colored Jones polynomial (which arise from the quantum ChernSimons theory of WittenReshetikhinTuraev) have a purely algebraic construction in terms of the representation theory of quantum groups. Despite this algebraic nature they appear to be connected to geometry: a class of related volume conjectures assert that their semiclassical asymptotics determine geometric invariants like the hyperbolic volume. To better understand these conjectures a number of authors have studied ways to twist quantum invariants by geometric data. In particular, Blanchet, Geer, PatureauMirand, and Reshetikhin recently defined quantum holonomy invariants depending on a link in S^3 and a flat 𝔰𝔩₂ connection on its complement. Their construction uses certain unusual cyclic modules of quantum 𝔰𝔩₂. For technical reasons the invariants are quite difficult to compute. In this talk (based on joint work with Nicolai Reshetikhin) I will explain how to effectively compute them using hyperbolic tensor networks constructed from quantum dilogarithms. Our construction reveals deep connections with hyperbolic geometry and suggests a way to break the KashaevMurakamiMurakami volume conjecture into two simpler pieces.

29430

Tuesday 11/15 3:00 PM

LouisHadrien Robert, Université Clermont Auvergne

Symmetric link homology
 LouisHadrien Robert, Université Clermont Auvergne
 Symmetric link homology
 11/15/2022
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
In this talk I will detail a construction of symmetric link
homology. In particular, this provides a nontrivial categorification of
1 and a finite dimensional categorification of the colored Jones
polynomial and a new categorification of the Alexander polynomial. I
will also explain how this relates to the triply graded homology and
knot Floer homology.

29448

Tuesday 11/29 3:00 PM

Justin Lanier, University of Chicago

Mapping class groups and dense conjugacy classes
 Justin Lanier, University of Chicago
 Mapping class groups and dense conjugacy classes
 11/29/2022
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Peter Kilgore Johnson (john8251@msu.edu)
I’ll start by introducing infinitetype surfaces—those with infinite genus or infinitely many punctures—and the emerging study of their mapping class groups. One difference from the finitetype setting is that these mapping class groups come with natural nondiscrete topologies. I’ll discuss joint work with Nick Vlamis where we fully characterize which surfaces have mapping class groups with dense conjugacy classes, so that there exists an element that well approximates every mapping class, up to conjugacy.

30446

Tuesday 12/6 3:00 PM

Cameron Gates Rudd, Max Planck Institute, Bonn

TBA
 Cameron Gates Rudd, Max Planck Institute, Bonn
 TBA
 12/06/2022
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
TBA
