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Talk_id	Date	Speaker	Title
15383	Thursday 1/17 2:00 PM	Chris Kottke, New College Florida	Compactification of monopole moduli spaces New Window Geometry and Topology Speaker: Chris Kottke, New College Florida Title: Compactification of monopole moduli spaces Date: 01/17/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall I will discuss joint work with Michael Singer and Karsten Fritzsch on compactifications of the moduli spaces $M_k$ of $\mathrm{SU}(2)$ magnetic monopoles on $\mathbf{R}^3$ . Via a geometric gluing procedure, we construct manifolds with corners compactifying the $M_k$ , the boundaries of which represent monopoles of charge $k$ decomposing into widely separated ‘monopole clusters' of lower charge. The hyperkahler metric on $M_k$ has a complete asymptotic expansion, the leading terms of which generalize the asymptotic metric discovered by Bielawski, Gibbons and Manton in the case that the monopoles are all widely separated. From the structure of the compactification, we are able to make partial progress toward proving Sen's conjecture for $L^2$ cohomology of the moduli spaces.
16468	Thursday 1/24 2:00 PM	Rebecca Winarski, University of Michigan	Solving the Twisted Rabbit Problem using trees New Window Geometry and Topology Speaker: Rebecca Winarski, University of Michigan Title: Solving the Twisted Rabbit Problem using trees Date: 01/24/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall The twisted rabbit problem is a celebrated problem in complex dynamics. Work of Thurston proves that up to equivalence, there are exactly three branched coverings of the sphere to itself satisfying certain conditions. When one of these branched coverings is modified by a mapping class, a map equivalent to one of the three coverings results. Which one? After remaining open for 25 years, this problem was solved by Bartholdi-Nekyrashevych using iterated monodromy groups. In joint work with Belk, Lanier, and Margalit, we present an alternate solution using topology and geometric group theory that allows us to solve a more general problem.
15394	Thursday 2/7 2:00 PM	Adam Sikora, SUNY at Buffalo	New Approach to Quantum Teichmuller Theory New Window Geometry and Topology Speaker: Adam Sikora, SUNY at Buffalo Title: New Approach to Quantum Teichmuller Theory Date: 02/07/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall The Jones polynomial invariant of links in R^3 extends to links in thickened surfaces, leading to the notion of the skein algebra of a surface, which is a version of Chekhov-Fock quantum Teichmuller space. The algebraic structure of skein algebras is quite rich and mysterious. We will approach it using the theory of measured foliations and pseudo-Anosov diffeomorphisms of surfaces
17499	Thursday 2/14 2:00 PM	Melissa Zhang, Boston College	Localization in Khovanov homology New Window Geometry and Topology Speaker: Melissa Zhang, Boston College Title: Localization in Khovanov homology Date: 02/14/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall When a topological object admits a group action, we expect that our invariants reflect this symmetry in their structure. This talk will tour the expression of link symmetries in three generations of related invariants: the Jones polynomial; its categorification, Khovanov homology; and the youngest invariant in the family, the Khovanov stable homotopy type, introduced by Lipshitz and Sarkar. I will describe how to use Lawson-Lipshitz-Sarkar's Burnside functor construction of the Lipshitz-Sarkar Khovanov homotopy type to produce localization theorems and Smith-type inequalities for the Khovanov homology of periodic links. This joint work with Matthew Stoffregen.
17505	Thursday 2/21 2:00 PM	Ilya Gekhtman , University of Toronto	Growth rates of invariant random subgroups of hyperbolic groups and rank 1 Lie groups. New Window Geometry and Topology Speaker: Ilya Gekhtman , University of Toronto Title: Growth rates of invariant random subgroups of hyperbolic groups and rank 1 Lie groups. Date: 02/21/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall Abstract: Invariant random subgroups (IRS) are conjugacy invariant probability measures on the space of subgroups of a given group G. They arise naturally as point stabilizers of probability measure preserving actions. The space of invariant random subgroups of SL_{2}R can be regarded as a natural compactification of the moduli space of Riemann surfaces, related to the Deligne-Mumford compactification. Invariant random subgroups can be regarded as a generalization both of normal subgroups and of lattices in topological groups. As such, it is interesting to extend results from the theories of normal subgroups and of lattices to the IRS setting. Jointly with Arie Levit, we prove such a result: the critical exponent (exponential growth rate) of an infinite IRS in an isometry group of a Gromov hyperbolic space (such as a rank 1 Lie group, or a hyperbolic group) is almost surely greater than half the Hausdorff dimension of the boundary. This generalizes an analogous result of Matsuzaki-Yabuki-Jaerisch for normal s As a corollary, we obtain that if $\Gamma$ is a typical subgroup and $X$ a rank 1 symmetric space then $\lambda_{0}(X/\Gamma)<\lambda_{0}(X)$ where $\lambda_0$ is the bottom of the spectrum of the Laplacian. The proof uses ergodic theorems for actions of hyperbolic groups. I will also talk about results about growth rates of normal subgroups of hyperbolic groups that inspired this work.
17509	Thursday 2/28 2:00 PM	Eva Belmont, Northwestern University	TBA New Window Geometry and Topology Speaker: Eva Belmont, Northwestern University Title: TBA Date: 02/28/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall No abstract available.
17537	Thursday 3/7 2:00 PM	SPRING BREAK	SPRING BREAK New Window Geometry and Topology Speaker: SPRING BREAK Title: SPRING BREAK Date: 03/07/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall No abstract available.
15423	Thursday 3/14 2:00 PM	Luca Spolaor, Massachusetts Institute of Technology	TBA New Window Geometry and Topology Speaker: Luca Spolaor, Massachusetts Institute of Technology Title: TBA Date: 03/14/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall No abstract available.
17538	Thursday 4/4 2:00 PM	Leonid Chekhov, MSU	TBA New Window Geometry and Topology Speaker: Leonid Chekhov, MSU Title: TBA Date: 04/04/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall No abstract available.
17510	Monday 4/8 3:00 PM	Mona Merling, University of Pennsylvania	TBA New Window Geometry and Topology Speaker: Mona Merling, University of Pennsylvania Title: TBA Date: 04/08/2019 Time: 3:00 PM - 4:00 PM Place: C304 Wells Hall No abstract available.
17498	Thursday 4/11 2:00 PM	Jennifer Hom, Georgia Tech	TBA New Window Geometry and Topology Speaker: Jennifer Hom, Georgia Tech Title: TBA Date: 04/11/2019 Time: 2:00 PM - 3:00 PM Place: C304 Wells Hall No abstract available.

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