Talk_id  Date  Speaker  Title 
15383

Thursday 1/17 2:00 PM

Chris Kottke, New College Florida

Compactification of monopole moduli spaces
 Chris Kottke, New College Florida
 Compactification of monopole moduli spaces
 01/17/2019
 2:00 PM  3:00 PM
 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
 Rebecca Winarski, University of Michigan
 Solving the Twisted Rabbit Problem using trees
 01/24/2019
 2:00 PM  3:00 PM
 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 BartholdiNekyrashevych 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

TBA
 Adam Sikora, SUNY at Buffalo
 TBA
 02/07/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

17499

Thursday 2/14 2:00 PM

Melissa Zhang, Boston College

TBA
 Melissa Zhang, Boston College
 TBA
 02/14/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

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.
 Ilya Gekhtman , University of Toronto
 Growth rates of invariant random subgroups of hyperbolic groups and rank 1 Lie groups.
 02/21/2019
 2:00 PM  3:00 PM
 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 DeligneMumford 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 MatsuzakiYabukiJaerisch 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
 Eva Belmont, Northwestern University
 TBA
 02/28/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

15423

Thursday 3/14 2:00 PM

Luca Spolaor, Massachusetts Institute of Technology

TBA
 Luca Spolaor, Massachusetts Institute of Technology
 TBA
 03/14/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.

17510

Monday 4/8 3:00 PM

Mona Merling, University of Pennsylvania

TBA
 Mona Merling, University of Pennsylvania
 TBA
 04/08/2019
 3:00 PM  4:00 PM
 C304 Wells Hall
No abstract available.

17498

Thursday 4/11 2:00 PM

Jennifer Hom, Georgia Tech

TBA
 Jennifer Hom, Georgia Tech
 TBA
 04/11/2019
 2:00 PM  3:00 PM
 C304 Wells Hall
No abstract available.
