Talk_id  Date  Speaker  Title 
13345

Thursday 9/6 2:00 PM

Alex Waldron, MSU

YangMills flow in dimension four
 Alex Waldron, MSU
 YangMills flow in dimension four
 09/06/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
Among the classical geometric evolution equations, YM flow is the least nonlinear and best behaved. Nevertheless, curvature concentration is a subtle problem when the base manifold has dimension four. I'll discuss my proof that finitetime singularities do not occur, and briefly describe the infinitetime picture.

13292

Thursday 9/13 2:00 PM

Rita Gitik, Michigan

On Tame Subgroups of Finitely Presented Groups
 Rita Gitik, Michigan
 On Tame Subgroups of Finitely Presented Groups
 09/13/2018
 2:00 PM  2:50 PM
 C304 Wells Hall
We describe several examples of tame subgroups of finitely presented groups and prove that the fundamental groups of certain finite graphs of groups are locally tame.

15396

Thursday 9/27 2:00 PM

Giuseppe Martone, University of Michigan

Hitchin representations and positive configurations of apartments
 Giuseppe Martone, University of Michigan
 Hitchin representations and positive configurations of apartments
 09/27/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
Hitchin singled out a preferred component in the character variety of representations from the fundamental group of a surface to PSL(d,R). When d=2, this Hitchin component coincides with the Teichm\"uller space consisting of all hyperbolic metrics on the surface. Later Labourie showed that Hitchin representations share many important differential geometric and dynamical properties.
Parreau extended previous work of Thurston and MorganShalen to a compactification of the Hitchin component whose boundary points are described by actions of the fundamental group of the surface on a building.
In this talk, we offer a new point of view for the Parreau compactification, which is based on certain positivity properties discovered by Fock and Goncharov. Specifically, we use the FockGoncharov construction to describe the intersection patterns of apartments in invariant subsets of the building that arises in the boundary of the Hitchin component.

14370

Thursday 10/4 2:00 PM

Artem Kotelskiy, Indiana University

Khovanov homology and BarNatan's deformation via immersed curves in the 4punctured sphere.
 Artem Kotelskiy, Indiana University
 Khovanov homology and BarNatan's deformation via immersed curves in the 4punctured sphere.
 10/04/2018
 2:00 PM  2:50 PM
 C304 Wells Hall
We will describe a geometric interpretation of Khovanov homology and its deformation due to BarNatan as Lagrangian Floer homology of two immersed curves in the 4punctured 2sphere S^2 \ 4pt. We will first start with a certain cobordism theoretic algebra H, where elements are all cobordisms between two trivial tangles )( and = up to certain relations. The central point then will be the observation that this algebra is isomorphic to an algebra B = Fuk(a0, a1), whose elements are generators of wrapped Lagrangian Floer complexes between two arcs a0 and a1 inside S^2 \ 4pt. The results will follow because D structures over H give Khovanov/BarNatan invariants for 4ended tangles, and D structures over B give curves in S^2 \ 4pt (due to [Haiden, Katzarkov, Kontsevich]).
The construction is originally inspired by a result of [Hedden, Herald, Hogancamp, Kirk], which embeds 4ended reduced Khovanov arc algebra (or, equivalently, BarNatan dotted cobordism algebra) into the Fukaya category of the 4punctured sphere. This is joint work with Liam Watson and Claudius Zibrowius.

15379

Thursday 10/11 2:00 PM

Matthew Stoffregen, MIT

An infiniterank summand of the homology cobordism group
 Matthew Stoffregen, MIT
 An infiniterank summand of the homology cobordism group
 10/11/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
This talk explains a generalization of the techniques that Hom introduced to construct an infiniterank summand of the topologically slice knot concordance group. We generalize Hom's epsiloninvariant to the involutive Heegaard Floer homology constructed by HendricksManolescu. As an application, we see that there is an infiniterank summand of the homology cobordism group, generated by Seifert spaces. The talk will contain a review of involutive Floer homology. This is joint work with Irving Dai, Jen Hom, and Linh Truong.

15434

Thursday 10/18 2:00 PM

Siddhi Krishna, Boston College

Taut Foliations, Positive 3Braids, and the LSpace Conjecture
 Siddhi Krishna, Boston College
 Taut Foliations, Positive 3Braids, and the LSpace Conjecture
 10/18/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
The LSpace Conjecture is taking the lowdimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3manifold Y. In particular, it predicts a 3manifold Y isn't "simple" from the perspective of HeegaardFloer homology if and only if Y admits a taut foliation. The reverse implication was proved by Ozsvath and Szabo. In this talk, we'll present a new theorem supporting the forward implication. Namely, we'll use branched surfaces to build taut foliations for manifolds obtained by surgery on positive 3braid closures. As an example, we'll construct taut foliations in every nonLspace obtained by surgery along the P(2,3,7) pretzel knot. No background in HeegaardFloer or foliation theories will be assumed.

16445

Thursday 10/18 3:10 PM

Min Hoon Kim, KIAS

A family of freely slice good boundary links
 Min Hoon Kim, KIAS
 A family of freely slice good boundary links
 10/18/2018
 3:10 PM  4:00 PM
 C304 Wells Hall
The still open topological surgery conjecture for 4manifolds is equivalent to the statement that all good boundary links are freely slice. In this talk, I will show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all previously known methods for freely slicing good boundary links with two or more components, and provides new freely slice links. This is joint work with Jae Choon Cha and Mark Powell.

15386

Thursday 10/25 2:00 PM

William Worden, Rice University

Generic veering triangulations are not geometric
 William Worden, Rice University
 Generic veering triangulations are not geometric
 10/25/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
Abstract: Every pseudoAnosov mapping class \phi deﬁnes an associated veering triangulation \tau_\phi of a punctured mapping torus. We show that generically, \tau_\phi is not geometric. Here, the word “generic” can be taken either with respect to random walks in mapping class groups or with respect to counting geodesics in moduli space. After describing how veering triangulations are obtained from pseudoAnosov maps, we will discuss some tools that go into the proof and give an outline if time permits.

15387

Thursday 11/1 11:00 AM

Yuanqi Wang

Moduli space of G2instantons on 7dimensional product manifolds
 Yuanqi Wang
 Moduli space of G2instantons on 7dimensional product manifolds
 11/01/2018
 11:00 AM  12:00 PM
 C304 Wells Hall
$G_2$instantons are 7dimensional analogues of flat
connections in dimension 3. It is part of DonaldsonThomas’ program to
generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8.
The moduli space of $G_2$instantons, with virtual dimension 0, is
expected to have interesting geometric structure and yield enumerative
invariant for the underlying 7dimensional manifold.
In this talk, in some reasonable special cases and a fairly complete manner,
we will describe the relation between the moduli space of $G_2$instantons
and an algebraic geometry moduli on a CalabiYau 3fold.

13346

Thursday 11/8 2:00 PM

Jonathan Campbell, Vanderbilt University

Topological Hochschild Homology and Higher Characters
 Jonathan Campbell, Vanderbilt University
 Topological Hochschild Homology and Higher Characters
 11/08/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
In this talk I'll explain how Hochschild homology and duality theory in bicategories can be used to obtain interesting Euler characteristictype invariants in a number of mathematical contexts (all of the terms in the previous sentence will be explained). A topological refinement, using THH, of this reasoning very easily yields interesting fixed point invariants, such as the Lefschetz trace and Reidemeister trace. Using this, one can show that the cyclotomic trace from algebraic Ktheory is computing fixed point invariants. Time permitting, I'll explain how zeta functions relate to the above. Prerequisites: an appetite for category theory, and a belief in, but not knowledge of, the stable homotopy category.

14374

Thursday 11/15 2:00 PM

Ian Zemke, Princeton University

The stabilization distance and knot Floer homology
 Ian Zemke, Princeton University
 The stabilization distance and knot Floer homology
 11/15/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
Given a knot K in S^3, we consider the set of oriented surfaces in B^4 which bound K. A natural question is how many stabilizations and destabilizations one must perform to move from one surface to another. Similarly, one may wonder how many double point birth/deaths must occur in a regular homotopy. In this talk, we consider several metrics on the set of surfaces bounding K, based on the number of stabilizations which must occur in a stabilization sequence connecting the two surfaces, or in the minimal number of double points which appear in a generic regular homotopy. We will describe how the link Floer TQFT can be used to construct lower bounds. This is joint work with Andras Juhasz.

15380

Thursday 11/29 2:00 PM

Dominic Culver, University of Illinois UrbanaChampaign

Towards a counter example of the telescope conjecture
 Dominic Culver, University of Illinois UrbanaChampaign
 Towards a counter example of the telescope conjecture
 11/29/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
The telescope conjecture is the only remaining Ravenel conjecture to remain unsolved. In this talk, I will give a review of the chromatic perspective on stable homotopy theory and motivate the telescope conjecture. I will then proceed to sketch Mahowald’s proof of the height 1 telescope conjecture for 2local spectra. Time permitting, I will describe work in progress with Beaudry, Behrens, Bhattacharya, and Xu on using the tmfresolution of the BhattacharyaEgger spectrum to find a counter example to the height 2 telescope conjecture.

15397

Thursday 12/6 2:00 PM

Lev TovstopyatNelip , Boston College

The transverse invariant and braid dynamics
 Lev TovstopyatNelip , Boston College
 The transverse invariant and braid dynamics
 12/06/2018
 2:00 PM  2:50 PM
 C304 Wells Hall
Let K be a link braided about an open book (B,p) supporting a contact manifold (Y,x). K and B are naturally transverse links. We prove that the hat version of the transverse link invariant defined by Baldwin, VelaVick and Vertesi is nonzero for the union of K with B. As an application, we prove that the transverse invariant of any braid having fractional Dehn twist coefficient greater than one is nonzero. We discuss geometric consequences and future directions.
