Abstracts
Week of September 8, 2019
Group Actions and Dynamics  Decrease of Fourier coefficients of Furstenberg measures and renewal theory 
4:15pm 
LOM206

Let mu be a Borel probability measure on SL(2,R) with a finite 
Geometry, Symmetry and Physics  Matroidal Schur algebras and category O 
4:30pm 
LOM 214

The category O of BernsteinGelfandGelfand and the Schur algebra are interesting and fundamental objects. Following motivation connected to 3dimensional supersymmetric gauge theory, BradenLicataProudfootWebster defined an analogue of category O associated to any hypertoric (aka toric hyperkahler) variety. In joint work with Braden, we use the same geometry to define analogues of the Schur algebra. In fact, we are able to define such an algebra starting from any matroid. In work in progress with Ethan Kowalenko, we extend the construction of BradenLicataProudfootWebster to a matroidal setting as well. In work in progress with Jens Eberhardt, we show that these matroidal Schur algebras and matroidal category O are related to each other via a categorification.

Algebra and Number Theory Seminar  padic equidistribution of CM points and applications 
4:15pm 
LOM 205

Abstract: Consider a sequence of CM points of increasing padic conductor on a modular curve X. What is its limiting distribution in any of the geometric incarnations of X? Works from the 2000s give the answer for the Riemann surface X(C), and for the reduction of X modulo primes different from p. I will describe the answer in the padic (Berkovich) analytic setting. A weak generalisation of this result has an application to the padic Birch and SwinnertonDyer conjecture. 
Geometry & Topology  Bounds on renormalized volume for Schottky manifolds 
4:15pm 
DL 431

During the talk I will introduce renormalized volume for convex cocompact hyperbolic 3manifolds and will also describe bounds for Schottky manifolds in term of extremal lengths in the conformal surface at infinity. This will be used to partially answer a question by Maldacena about comparing renormalized volume for Schottky and Fuchsian manifolds with the same conformal boundaries. 
Undergraduate Seminar  Putnam seminar 
6:30pm 
LOM 214/215
LOM 214/215
LOM 214/215
LOM 214/215
LOM 214/215
LOM 214/215
LOM 214/215
LOM 214/215
LOM 214/215
LOM 214/215
LOM 214/215

Weekly event for interested students to practice competition math problems in a relaxed setting. Meetings are held every Wednesday from 6:30pm to 8 in LOM 215. All are welcome to attend. Contact Pat Devlin to find out more. 
Combinatorics Seminar  Approximate SpielmanTeng theorems 
4:00pm 
DL 431

An approximate SpielmanTeng theorem for the least singular value $s_n(M_n)$ of a random $n\times n$ matrix $M_n$ is a statement of the following form: there exist constants $C,c > 0$ such that for all $\eta \geq 0$, $\mathbb{P}(s_n(M_n) \leq \eta) \lesssim n^{C}\eta + \exp(n^{c})$. I will discuss a novel combinatorial approach for proving such theorems in a fairly unified manner for a variety of random matrix models. 