Talk_id  Date  Speaker  Title 
6187

Thursday 1/25 2:00 PM

Siqi He, Caltech

The Extended Bogomolny Equations and Teichmuller space
 The Extended Bogomolny Equations and Teichmuller space
 01/25/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Siqi He, Caltech
We will discuss Witten’s gauge theory approach to Jones polynomial and Khovanov homology by counting solutions to some gauge theory equations with singular boundary conditions. When we reduce these equations to 3dimensional, we call them the extended Bogomolny equations. We will discuss a DonaldsonUlenbeckYau type correspondence of the moduli space of the singular solutions to the Extended Bogomolny equations and Teichmuller space. If time permits, we will also discuss the relationship of the singular solutions moduli space with higher Teichmuller theory. This is joint work with Rafe Mazzeo.

9247

Thursday 2/1 2:00 PM

Guillem Cazassus, Indiana University

Towards extended Floer field theories
 Towards extended Floer field theories
 02/01/2018
 2:00 PM  2:50 PM
 C304 Wells Hall
 Guillem Cazassus, Indiana University
Donaldson polynomials are powerful invariants associated to smooth fourmanifolds. The introduction by Floer of Instanton homology groups, associated to some 3manifolds, allowed to define analogs of such polynomials for (some) fourmanifolds with boundary, that have a structure similar with a TQFT.
Wehrheim and Woodward developed a framework called "Floer field theory" which, according to the AtiyahFloer conjecture, should permit to recover Donaldson invariants from a 2functor from the 2category Cob_{2+1+1} to a 2category Symp they defined, which is an enrichment of Weinstein's symplectic category.
I will describe a framework that should permit to extend such a 2functor to lower dimensions. This framework should permit to define new invariants in Manolescu and Woodward's symplectic instanton homology (sutured theory, equivariant version). This is work in progress.

8243

Tuesday 2/6 2:00 PM

Boyu Zhang, Harvard University

Rectifiability and Minkowski bounds for the singular sets of multiplevalued harmonic spinors
 Rectifiability and Minkowski bounds for the singular sets of multiplevalued harmonic spinors
 02/06/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Boyu Zhang, Harvard University
We prove that the singular set of a multiplevalued harmonic spinor on a 4manifold is 2rectifiable and has finite Minkowski content. This result improves a regularity result of Taubes in 2014. It implies more precise descriptions for the limit behavior of nonconvergent sequences of solutions to many important gaugetheoretic equations, such as the KapustinWitten equations, the VafaWitten equations, and the SeibergWitten equations with multiple spinors.

8237

Thursday 3/1 2:00 PM

Matthias Nagel, McMaster University, Canada

Triple linking numbers and surface systems
 Triple linking numbers and surface systems
 03/01/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Matthias Nagel, McMaster University, Canada
We relate fillability of two link exteriors,
and the question when two links admit homeomorphic
surface systems to (a refinement of) Milnor’s triple
linking numbers. This extends a theorem of DavisRoth
to include also links with nonvanishing linking numbers.
This is joint work with C. Davis, P. Orson, and M. Powell.

9245

Thursday 3/8 2:00 PM

No seminar

Spring Break
 Spring Break
 03/08/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 No seminar
No abstract available.

12282

Thursday 3/15 2:00 PM

Kristen Hendricks, MSU

Connected Heegaard Floer homology and homology cobordism
 Connected Heegaard Floer homology and homology cobordism
 03/15/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Kristen Hendricks, MSU
We study applications of Heegaard Floer homology to homology cobordism. In particular, to a homology sphere Y, we define a module HF_conn(Y), called the connected Heegaard Floer homology of Y, and show that this module is invariant under homology cobordism and isomorphic to a summand of HF_red(Y). The definition of this invariant relies on involutive Heegaard Floer homology. We use this to define a new filtration on the homology cobordism group, and to give a reproof of Furuta's theorem. This is joint work with Jen Hom and Tye Lidman.

7202

Thursday 3/22 2:00 PM

Adam Lowrance, Vassar College

Almost alternating, Turaev genus one, and semiadequate links
 Almost alternating, Turaev genus one, and semiadequate links
 03/22/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Adam Lowrance, Vassar College
A link is almost alternating if it is nonalternating and has a diagram such that one crossing change transforms it into an alternating diagram. Turaev genus one links are a certain generalization of nonalternating Montesinos links. A link is semiadequate if it has a diagram where at least one of the allA or allB Kauffman state graphs is loopless. In this talk, we discuss the Jones polynomial and Khovanov homology of links in these three classes, and we discuss open problems about the relationships between the three classes.

9243

Thursday 3/29 2:00 PM

Ramanujan Santharoubane, University of Virginia

Asymptotic of quantum representations of surface groups
 Asymptotic of quantum representations of surface groups
 03/29/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Ramanujan Santharoubane, University of Virginia
In a previous work with Thomas Koberda we defined actions of surface groups on the vector spaces coming from the WittenReshetikhinTuraev TQFT. For l a given loop in a surface we can define the trace of the associated operator. Actually, this is a sequence of invariant depending on a sequence of roots of unity. For any z on the unit circle, we study the asymptotic of this sequence of invariant when the sequence of roots of unity converges to z. The main theorem says that this asymptotic is determined by the evaluation at z of a Laurent polynomial depending only on l. This polynomial can be viewed as a Jones polynomial for surface groups. The main corollary concerns the socalled AMU conjecture which relates TQFT representations of mapping class groups to the NielsenThurston classification.
This talk represent a joint work with Julien Marché.

9246

Thursday 4/5 2:00 PM

Juanita PinzonCalcedo, North Carolina State

Gauge Theory and Knot Concordance
 Gauge Theory and Knot Concordance
 04/05/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Juanita PinzonCalcedo, North Carolina State
Knot concordance can be regarded as the study of knots as boundaries of surfaces embedded in spaces of dimension 4. Specifically, two knots K_0 and K_1 are said to be smoothly concordant if there is a smooth embedding of the 2dimensional annulus S^1 × [0, 1] into the 4dimensional cylinder S^3 × [0, 1] that restricts to the given knots at each end. Smooth concordance is an equivalence relation, and the set of smooth concordance classes of knots, C, is an abelian group with connected sum as the binary operation. The algebraic structure of C, the concordance class of the unknot, and the set of knots that are topologically slice but not smoothly slice are much studied objects in lowdimensional topology. Gauge theoretical results on the nonexistence of certain definite smooth 4manifolds can be used to better understand these objects. In this talk I will explain how the study of instantons can be used to shown that (1) the group of topologically slice knots up to smooth concordance contains a subgroup isomorphic to Z^\infty, and (2) satellite operations that are similar to cables are not homomorphisms on C.

13297

Tuesday 4/10 2:00 PM

Aleksander Doan, Stony Brook University

SeibergWitten monopoles with multiple spinors on a surface times a circle
 SeibergWitten monopoles with multiple spinors on a surface times a circle
 04/10/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Aleksander Doan, Stony Brook University
I will discuss a generalisation of the 3dimensional SeibergWitten equations which was studied by Haydys and Walpuski in relation to YangMills theory on manifolds with special holonomy. The main difference from the classical setting is the noncompactness of the moduli space of solutions. I will explain how to tackle this problem and count the solutions in the special case when the underlying 3manifold is the product of a Riemann surface and a circle. The main ingredient is a holomorphic description of the moduli space of solutions and its compactification. It allows us to relate our problem to classical results on holomorphic vector bundles on Riemann surfaces.

9244

Thursday 4/12 2:00 PM

Adam Saltz, University of Georgia

Link homology and Floer homology in pictures
 Link homology and Floer homology in pictures
 04/12/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Adam Saltz, University of Georgia
There are no fewer than eight link homology theories which admit spectral sequences from Khovanov homology. These theories have very different origins  representation theory, gauge theory, symplectic topology  so it's natural to ask for some kind of unifying theory. I will attempt to describe this theory using BarNatan's pictorial formulation of link homology. This strengthens a result of Baldwin, Hedden, and Lobb and proves new functoriality results for several link homology theories. It may also be useful for studying mutation. (I won't assume much specific knowledge of these link homology theories!)

9262

Thursday 4/19 2:00 PM

Calvin Woo, Indiana University

Topological Hochschild homology and logarithmic geometry
 Topological Hochschild homology and logarithmic geometry
 04/19/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Calvin Woo, Indiana University
While a need to compute algebraic Ktheory led topologists to consider spectrallyenriched versions of Hochschild homology, over the years topological Hochschild homology (THH) has emerged as an interesting invariant in its own right. In this talk, I will introduce some of these interesting properties and show how logarithmic geometry can help us shine light on THH's arithmetic structure.

13338

Monday 4/23 4:10 PM


Dylan Thurston, title TBA
 Dylan Thurston, title TBA
 04/23/2018
 4:10 PM  5:00 PM
 C304 Wells Hall

No abstract available.
