| Talk_id | Date | Speaker | Title |
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13345
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Thursday 9/6
2:00 PM
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Alex Waldron, MSU
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Yang-Mills flow in dimension four
- Alex Waldron, MSU
- Yang-Mills 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 finite-time singularities do not occur, and briefly describe the infinite-time picture.
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13292
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Thursday 9/13
2:00 PM
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Rita Gitik, Michigan
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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.
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15396
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Thursday 9/27
2:00 PM
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Giuseppe Martone, University of Michigan
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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 Morgan-Shalen 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 Fock-Goncharov construction to describe the intersection patterns of apartments in invariant subsets of the building that arises in the boundary of the Hitchin component.
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14370
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Thursday 10/4
2:00 PM
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Artem Kotelskiy, Indiana University
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Khovanov homology and Bar-Natan's deformation via immersed curves in the 4-punctured sphere.
- Artem Kotelskiy, Indiana University
- Khovanov homology and Bar-Natan's deformation via immersed curves in the 4-punctured 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 Bar-Natan as Lagrangian Floer homology of two immersed curves in the 4-punctured 2-sphere 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/Bar-Natan invariants for 4-ended 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 4-ended reduced Khovanov arc algebra (or, equivalently, Bar-Natan dotted cobordism algebra) into the Fukaya category of the 4-punctured sphere. This is joint work with Liam Watson and Claudius Zibrowius.
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15379
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Thursday 10/11
2:00 PM
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Matthew Stoffregen, MIT
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An infinite-rank summand of the homology cobordism group
- Matthew Stoffregen, MIT
- An infinite-rank 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 infinite-rank summand of the topologically slice knot concordance group. We generalize Hom's epsilon-invariant to the involutive Heegaard Floer homology constructed by Hendricks-Manolescu. As an application, we see that there is an infinite-rank 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.
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15434
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Thursday 10/18
2:00 PM
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Siddhi Krishna, Boston College
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Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
- Siddhi Krishna, Boston College
- Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
- 10/18/2018
- 2:00 PM - 3:00 PM
- C304 Wells Hall
The L-Space Conjecture is taking the low-dimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3-manifold Y. In particular, it predicts a 3-manifold Y isn't "simple" from the perspective of Heegaard-Floer 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 3-braid closures. As an example, we'll construct taut foliations in every non-L-space obtained by surgery along the P(-2,3,7) pretzel knot. No background in Heegaard-Floer or foliation theories will be assumed.
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16445
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Thursday 10/18
3:10 PM
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Min Hoon Kim, KIAS
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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 4-manifolds 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.
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15386
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Thursday 10/25
2:00 PM
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William Worden, Rice University
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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 pseudo-Anosov 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 pseudo-Anosov maps, we will discuss some tools that go into the proof and give an outline if time permits.
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15387
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Thursday 11/1
11:00 AM
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Yuanqi Wang
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Moduli space of G2-instantons on 7-dimensional product manifolds
- Yuanqi Wang
- Moduli space of G2-instantons on 7-dimensional product manifolds
- 11/01/2018
- 11:00 AM - 12:00 PM
- C304 Wells Hall
$G_2$-instantons are 7-dimensional analogues of flat
connections in dimension 3. It is part of Donaldson-Thomas’ 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 7-dimensional 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 Calabi-Yau 3-fold.
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13346
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Thursday 11/8
2:00 PM
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Jonathan Campbell, Vanderbilt University
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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 characteristic-type 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 K-theory 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.
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14374
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Thursday 11/15
2:00 PM
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Ian Zemke, Princeton University
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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.
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15380
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Thursday 11/29
2:00 PM
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Dominic Culver, University of Illinois Urbana-Champaign
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Towards a counter example of the telescope conjecture
- Dominic Culver, University of Illinois Urbana-Champaign
- 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 2-local spectra. Time permitting, I will describe work in progress with Beaudry, Behrens, Bhattacharya, and Xu on using the tmf-resolution of the Bhattacharya-Egger spectrum to find a counter example to the height 2 telescope conjecture.
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15397
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Thursday 12/6
2:00 PM
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Lev Tovstopyat-Nelip , Boston College
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The transverse invariant and braid dynamics
- Lev Tovstopyat-Nelip , 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, Vela-Vick and Vertesi is non-zero 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 non-zero. We discuss geometric consequences and future directions.
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