Talk_id  Date  Speaker  Title 
31527

Tuesday 1/10 2:30 PM


G&T Seminar Organizational Meeting

 G&T Seminar Organizational Meeting
 01/10/2023
 2:30 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
No abstract available.

31562

Tuesday 2/7 3:30 PM

Amitesh Datta, Princeton University

Does the Jones polynomial of a knot detect the unknot? A novel approach via braid group representations and class numbers of number fields.
 Amitesh Datta, Princeton University
 Does the Jones polynomial of a knot detect the unknot? A novel approach via braid group representations and class numbers of number fields.
 02/07/2023
 3:30 PM  4:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Peter Kilgore Johnson (john8251@msu.edu)
How good of an invariant is the Jones polynomial? The question is closely tied to studying braid group representations since the Jones polynomial can be defined as a (normalized) trace of a braid group representation.
In this talk, I will present my work developing a new theory to precisely characterize the entries of classical braid group representations, which leads to a generic faithfulness result for the Burau representation of B_4 (the faithfulness is a longstanding question since the 1930s and is equivalent to whether B_4 is a group of 3 x 3 matrices). In forthcoming work, I use this theory to furthermore explicitly characterize the Jones polynomial of all 3braid closures and generic 4braid closures. I will also describe my work which uses the class numbers of quadratic number fields to show that the Jones polynomial detects the unknot for 3braid links  this work also answers (in a strong form) a question of Vaughan Jones.
I will discuss all of the relevant background from scratch and illustrate my techniques through simple examples.

31504

Tuesday 2/14 2:00 PM

Renaud Detcherry, Institut de Mathématiques de Bourgogne

Title: On the kernel of WittenReshetikhinTuraev quantum representations
 Renaud Detcherry, Institut de Mathématiques de Bourgogne
 Title: On the kernel of WittenReshetikhinTuraev quantum representations
 02/14/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Efstratia Kalfagianni (kalfagia@msu.edu)
Abstract: WittenReshetikhinTuraev SO(3) quantum representations are a family of representations of mapping class groups of surfaces. The family is asymptotically faithful, but each representation has kernel: indeed, rth powers of Dehn twists are in the kernel of the level r quantum representation.
An open question is whether the kernel is generated by rth powers of Dehn twists; we will present partial results on this question, by relating the socalled "hadic expansion" of quantum representations to Johnson homomorphisms.

31556

Tuesday 2/21 2:00 PM

Ian Montague , Brandeis University

SeibergWitten Floer KTheory and Cyclic Group Actions
 Ian Montague , Brandeis University
 SeibergWitten Floer KTheory and Cyclic Group Actions
 02/21/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
Given a spin rational homology sphere equipped with a cyclic group action, I will introduce equivariant refinements of Manolescu's kappa invariant, derived from the equivariant Ktheory of the SeibergWitten Floer spectrum. These invariants give rise to equivariant relative 10/8ths type inequalities for equivariant spin cobordisms between rational homology spheres. I will explain how these inequalities provide applications to knot concordance, obstruct cyclic group actions on spin fillings, and give genus bounds for knots in punctured 4manifolds. If time permits I will explain how these invariants are related to equivariant etainvariants of the Dirac operator, and describe workinprogress which provides explicit formulas for the $S^1$equivariant etainvariants on Seifertfibered spaces.

31547

Tuesday 2/28 2:00 PM

Ryan Stees, Indiana University

Milnor's invariants for knots and links in closed orientable 3manifolds
 Ryan Stees, Indiana University
 Milnor's invariants for knots and links in closed orientable 3manifolds
 02/28/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
Early in his career, John Milnor defined his seminal link invariants, now called Milnor's $\overline{\mu}$invariants. They are topological concordance invariants of links in $S^3$, and much is known about them. However, until recently, few results have extended Milnor's work to links in other closed orientable 3manifolds, and such extensions have done so for special classes of 3manifolds or specific types of links. In this talk, I will discuss an extension of these invariants to concordance invariants of knots and links in any closed orientable 3manifold, discuss some theorems that justify calling them ``Milnor's invariants", and study their properties.

31573

Tuesday 3/14 11:30 AM

Shunyu Wan , University of Virginia

Naturality of Legendrian LOSS invariant under positive contact surgery and application
 Shunyu Wan , University of Virginia
 Naturality of Legendrian LOSS invariant under positive contact surgery and application
 03/14/2023
 11:30 AM  12:30 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
Given a Legendrian Knot L in a contact 3 manifold, one can associate a socalled LOSS invariant to L which lives in the knot Floer homology group. We prove that the LOSS invariant is natural under the positive contact surgery. In this talk I will review some background and definition, get the idea of the proof and try to focus on the application which is about new examples of nonsimple knots.

32601

Tuesday 3/14 2:00 PM

John Baldwin, Boston College

Small Dehn surgery and SU(2)representations
 John Baldwin, Boston College
 Small Dehn surgery and SU(2)representations
 03/14/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Matthew Edward Hedden (heddenma@msu.edu)
In their celebrated proof of the Property P Conjecture and its sequel, Kronheimer and Mrowka proved that the fundamental group of rsurgery on a nontrivial knot in the 3sphere admits an irreducible SU(2)representation whenever r is at most 2 in absolute value (which implies in particular that surgery on a nontrivial knot is never a homotopy 3sphere). They asked whether the same is true for other small values of r  in particular, for r = 3 and 4  noting that it's false for r = 5 since 5surgery on the righthanded trefoil is a lens space. I'll describe recent work which answers their question in the affirmative. Our proof involves Floer homology and also the dynamics of surface homeomorphisms. All of this work is joint with Steven Sivek, and significant parts are also joint with Zhenkun Li and Fan Ye.

31548

Monday 3/20 2:00 PM

Siddhi Krishna, Columbia University

RTG Seminar: Fibered knots: what, why and how
 Siddhi Krishna, Columbia University
 RTG Seminar: Fibered knots: what, why and how
 03/20/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
Fibered knots show up all over lowdimensional topology, as they provide a robust way to investigate interactions between phenomena of different dimensions. In this talk, I'll survey what they are, why you should care, and how to identify them. Then, as time permits, I'll also sketch a proof that positive braid knots are fibered. I will assume very little background for this talk  all are welcome!

31549

Tuesday 3/21 11:30 AM

Siddhi Krishna, Columbia University

Twist positivity, Lspace knots, and concordance
 Siddhi Krishna, Columbia University
 Twist positivity, Lspace knots, and concordance
 03/21/2023
 11:30 AM  12:30 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
In this talk, I’ll describe a braid word theoretic property, called “twist positivity”, which often puts strong restrictions on quantitative and geometric properties of a braid. I’ll describe some old and new results about twist positivity, as well as some new applications towards knot concordance. In particular, I’ll describe how using a suite of numerical knot invariants (including the braid index) in tandem allows one to prove that there is an infinite family of Lspace knots (containing all positive torus knots and also an infinite family of hyperbolic knots) where every knot represents a distinct smooth concordance class. This confirms a prediction of the sliceribbon conjecture. Everything I’ll discuss is joint work with Hugh Morton. I will assume little background about knot invariants for this talk – all are welcome!

31538

Tuesday 3/21 2:00 PM

Anup Poudel, Ohio State

A comparison between $SL_n$ spider categories.
 Anup Poudel, Ohio State
 A comparison between $SL_n$ spider categories.
 03/21/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Vijay B Higgins (higgi231@msu.edu)
In this talk, we will explore and make comparisons between various models that exist for spherical tensor categories associated to the category of representations of the quantum group $U_q(sl_n).$ In particular, we will discuss the combinatorial model of MurakamiOhtsukiYamada (MOY), the nvalent ribbon model of Sikora and the trivalent spider category of CautisKamnitzerMorrison (CKM). We conclude by showing that the full subcategory of the spider category from CKM, whose objects are monoidally generated by the standard representation and its dual, is equivalent as a spherical braided category to Sikora's quotient category. This proves a conjecture of Le and Sikora and also answers a question from Morrison's Ph.D. thesis.

31554

Tuesday 4/4 2:00 PM

David Chan, Vanderbilt University

TBA
 David Chan, Vanderbilt University
 TBA
 04/04/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
No abstract available.

31543

Monday 4/10 2:00 PM

Sam Gunningham, Montana State

RTG Seminar: TBA
 Sam Gunningham, Montana State
 RTG Seminar: TBA
 04/10/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Vijay B Higgins (higgi231@msu.edu)
TBA

31542

Tuesday 4/11 2:00 PM

Sam Gunningham, Montana State

TBA
 Sam Gunningham, Montana State
 TBA
 04/11/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Vijay B Higgins (higgi231@msu.edu)
TBA

32612

Tuesday 4/18 2:00 PM

PierreLouis Blayac, University of Michigan

TBA
 PierreLouis Blayac, University of Michigan
 TBA
 04/18/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Vijay B Higgins (higgi231@msu.edu)
TBA

31537

Monday 4/24 2:00 PM

Sarah Petersen, University of Colorado, Boulder

RTG Seminar: TBA
 Sarah Petersen, University of Colorado, Boulder
 RTG Seminar: TBA
 04/24/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
No abstract available.

31536

Tuesday 4/25 2:00 PM

Sarah Petersen, University of Colorado, Boulder

TBA
 Sarah Petersen, University of Colorado, Boulder
 TBA
 04/25/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
No abstract available.
