Talk_id  Date  Speaker  Title 
26968

Tuesday 1/26 2:50 PM

Matt Stoffregen, MSU

Surgery Exact Triangles in Involutive Floer homology
 Matt Stoffregen, MSU
 Surgery Exact Triangles in Involutive Floer homology
 01/26/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
We'll sketch the definition of the involutive Heegaard Floer homology constructed by HendricksManolescu, and then explain how this homology theory behaves under surgery. As a consequence, we can use the surgery formula to construct threemanifolds which are not homology cobordant to any combination of Seifert fiber spaces. This is joint work Kristen Hendricks, Jen Hom and Ian Zemke.

26986

Tuesday 2/2 2:50 PM

Dogancan Karabas, Northwestern University

Wrapped Fukaya category via gluing sheaves, and the case of pinwheels
 Dogancan Karabas, Northwestern University
 Wrapped Fukaya category via gluing sheaves, and the case of pinwheels
 02/02/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
In this talk, I will discuss some gluing techniques for microlocal sheaves, and calculate wrapped Fukaya category of some rational homology balls, which are quotients of $A_n$ Milnor fibres, via gluing sheaves on their skeleta, i.e. pinwheels.

26942

Tuesday 2/9 2:50 PM

Irving Dai, MIT

Lattice homology and instantons
 Irving Dai, MIT
 Lattice homology and instantons
 02/09/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
We show that if Y is the boundary of an almostrational plumbing, then the framed instanton Floer homology of Y is isomorphic to its Heegaard Floer homology. This class of 3manifolds includes all Seifert fibered rational homology spheres. Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps established by John Baldwin and Steven Sivek. This is joint work with Antonio Alfieri, John Baldwin, and Steven Sivek.

26953

Tuesday 2/16 2:50 PM

Linh Truong, University of Michigan

Upsilon invariant and rightveering open book decompositions
 Linh Truong, University of Michigan
 Upsilon invariant and rightveering open book decompositions
 02/16/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
In 2010, Hedden showed that the OzsvathSzabo concordance invariant tau can detect whether a fibered knot induces the tight contact structure on the threesphere. In 2017, OzsvathStipsiczSzabo constructed a oneparameter family of concordance invariants Upsilon, which recovers tau as a special case. I will discuss a sufficient condition using Upsilon for the monodromy of the open book decomposition of a fibered knot to be rightveering. As an application, I will discuss a generalization of Baker's conjecture on the concordance of tight, fibered knots. This is joint work with Dongtai He and Diana Hubbard.

26951

Tuesday 2/23 2:50 PM

Thang Le, Georgia Tech

Quantum trace map for $SL_n$ skein algebras of surfaces
 Thang Le, Georgia Tech
 Quantum trace map for $SL_n$ skein algebras of surfaces
 02/23/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
For a punctured surface there are two quantizations of the $SL_n$ character variety. The first quantization is the $SL_n$ skein algebra, and the second one is the quantization of the higher Teichmuller space.
When $n=2$ Bonahon and Wong showed that there is an algebra homomorphism, called the quantum trace, from the first quantized algebra to the second one. We show for general n a similar quantum trace map exists.
The construction of the $SL_n$ quantum trace is based on the theory of stated $SL_n$ skein algebra, developed in a joint work with A. Sikora, and a work of Chekhov and Shapiro.

26967

Tuesday 3/2 2:50 PM

Break Day, no talk

No talk
 Break Day, no talk
 No talk
 03/02/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
 Honghao Gao (gaohongh@msu.edu)
No abstract available.

26966

Tuesday 3/9 2:50 PM

Roger Casals, UC Davis

Lagrangian Fillings of Legendrian links: Two Constructions in Floer Theory
 Roger Casals, UC Davis
 Lagrangian Fillings of Legendrian links: Two Constructions in Floer Theory
 03/09/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
In this talk I will review our current understanding in the classification of Lagrangian fillings for Legendrian links in the standard contact 3sphere. The talk will present two illustrative constructions: one explaining how to build and detect infinitely many Lagrangian fillings using the Legendrian Contact DGA, and the other explaining how to classify fillings for the Hopf link using pseudoholomorphic foliations. First, I will present the basic objects of interest and survey the recent developments in the field (work with H. Gao, and work with E. Zaslow). Then I will delve into new and inprogress results on the Legendrian Contact DGA (work with L. Ng). Finally, I will report on how pseudoholomorphic curves might help us classify Lagrangian fillings in certain cases. During the course of the talk, I will try to highlight some of the interesting open questions and new methods that arise from our current work as well as future directions.

26978

Tuesday 3/16 2:50 PM

Keegan Boyle, UBC

Equivariant genera of strongly invertible knots
 Keegan Boyle, UBC
 Equivariant genera of strongly invertible knots
 03/16/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
Given a knot $K$, the minimum genus of an orientable surface embedded in $S^3$ or $B^4$ with boundary $K$ is a natural measure of knot complexity. In this talk I will generalize this idea to involutions on knots, focusing on the case where the involution preserves the orientation of $S^3$, but reverses the orientation of $K$. This talk is elementary in nature and will be very accessible. This is joint work with Ahmad Issa.

26992

Tuesday 3/23 2:50 PM

Samantha Allen, Dartmouth

Using surgery to study unknotting with a single twist
 Samantha Allen, Dartmouth
 Using surgery to study unknotting with a single twist
 03/23/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
Ohyama showed that any knot can be unknotted by performing two full twists, each on a set of parallel strands. We consider the question of whether or not a given knot can be unknotted with a single full twist, and if so, what are the possible linking numbers associated to such a twist. It is observed that if a knot can be unknotted with a single twist, then some surgery on the knot bounds a rational homology ball. Using tools such as classical invariants and invariants arising from Heegaard Floer theory, we give obstructions for a knot to be unknotted with a single twist of a given linking number. In this talk, I will discuss some of these obstructions, their implications (especially for alternating knots), many examples, and some unanswered questions. This talk is based on joint work with Charles Livingston.

26980

Tuesday 3/30 11:00 AM

Renaud Detcherry, Bourgogne

A quantum obstruction to purely cosmetic surgeries
 Renaud Detcherry, Bourgogne
 A quantum obstruction to purely cosmetic surgeries
 03/30/2021
 11:00 AM  11:50 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
The cosmetic surgery conjecture asks whether it is possible that two Dehnsurgeries on the same nontrivial knot in S³ give the same oriented 3manifolds. We will present new obstructions for a knot to admit purely cosmetic surgeries, using ReshetikhinTuraev invariants. In particular, we will show that if a knot admits purely cosmetic surgeries, then the slopes of the surgery are +1/5k unless the Jones polynomial of K is 1 at the fifth root of unity.

26979

Tuesday 4/6 2:50 PM

Charlie Frohman, U Iowa

A Geometric Kauffman Bracket
 Charlie Frohman, U Iowa
 A Geometric Kauffman Bracket
 04/06/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
This is joint work with Joanna KaniaBartoszynska and Thang Le $\\$
I will discuss the representation theory of the Kauffman bracket skein algebra of a finite type surface at a root of unity whose order is not divisible by 4. $\\$
Specifically, the Kauffman bracket skein algebra is an algebra with trace in the sense of De Concini, Procesi, Reshetikhin and Rosso, so it has a well defined character variety of trace preserving representations, which can be identified with a branched cover of the SL(2,C)character variety of the fundamental group of the underlying surface. $\\$
In the case of a closed surface the branched cover is trivial so its just the character variety of the fundamental group of the surface. $\\$
The skein algebra is also a Poisson order, so the character variety representations of the Kauffman bracket skein algebra of a closed surface decomposes into representations corresponding to irreducible, abelian and central representations of the fundamental group of the underlying surface. The irreducible representations of the fundamental group of the surface correspond to irreducible representations of the skein algebra. $\\$
We then use this as basic data to define an invariant of framed links in a threemanifold equipped with an irreducible representation of its fundamental group. The invariant satisfies the Kauffman bracket skein relations. $\\$
Such a representation could be the lift of the holonomy of a hyperbolic structure on the threemanifold, hence the title : A Geometric Kauffman Bracket. $\\$

26972

Tuesday 4/13 2:50 PM

Mustafa Hajij, Santa Clara University

AlgebraicallyInformed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
 Mustafa Hajij, Santa Clara University
 AlgebraicallyInformed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
 04/13/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
One of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from observed data. In this work, we make one step towards building a bridge between algebraic structures and deep learning, and introduce\textbf {AIDN},\textit {AlgebraicallyInformed Deep Networks}.\textbf {AIDN} is a deep learning algorithm to represent any finitelypresented algebraic object with a set of deep neural networks. The deep networks obtained via\textbf {AIDN} are\textit {algebraicallyinformed} in the sense that they satisfy the algebraic relations of the presentation of the algebraic structure that serves as the input to the algorithm. Our proposed network can robustly compute linear and nonlinear representations of most finitelypresented algebraic structures such as groups, associative algebras, and Lie algebras. We evaluate our proposed approach and demonstrate its applicability to algebraic and geometric objects that are significant in lowdimensional topology. In particular, we study solutions for the YangBaxter equations and their applications on braid groups. Further, we study the representations of the TemperleyLieb algebra. Finally, we show, using the ReshetikhinTuraev construction, how our proposed deep learning approach can be utilized to construct new link invariants. We believe the proposed approach would tread a path toward a promising future research in deep learning applied to algebraic and geometric structures.

26982

Tuesday 4/20 2:50 PM

Hannah Schwartz, Princeton

TBA
 Hannah Schwartz, Princeton
 TBA
 04/20/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
TBA

27026

Tuesday 4/27 2:50 PM

David Gay, University of Georgia

TBA
 David Gay, University of Georgia
 TBA
 04/27/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
TBA
