Upcoming Events

In a paper a few years ago with Akshay Venkatesh and Craig Westerland, we explained how to use results on stable cohomology of Hurwitz spaces to derive results about the variation of class groups in families of quadratic extensions of rational function fields over finite fields (i.e. we said…

It is well known from the pioneering work by H. McKean that the Fisher-KPP equation can be described in terms of the binary branching Brownian motion. It turns out that this elegant interpretation can be extended to a large class of parabolic equations, and systems of parabolic equations, via…

Bordered Floer homology is a suite of smooth invariants which associates to each 3-manifold with (parametrized) boundary a collection of modules of various types. In its simplest incarnation, the object CFD(Y) associated to a manifold Y with connected boundary can be thought of as a dg-module. A…

Abstract: In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. One way to introduce confinement to the equations is by imposing a negative value for the cosmological constant and study the evolution of solutions with Anti-de Sitter asymptotics…

We will present a quantitative signal subspace imaging method. This imaging method is a generalization of MUSIC that uses both the noise and signal subspaces of the data. The noise subspace provides high spatial resolution while the signal subspace provides quantitative information about the…

In this talk, we discuss the asymptotic behavior of the number of partitions into a fixed subset of positive integers. The main focus of the talk will be when this subset consists of primes concerning a Chebotarev condition. In special cases, this reduces to partitions into primes in arithmetic…

Abstract

Given a manifold (Mn;[h]), when is it the boundary of a conformally compact Einstein manifold (X^{n+1}; g+) with r^2g+ |_M = h for some defining function r on X^{n+1}? This problem of finding ”conformal filling in” is motivated by problems in the AdS/CFT correspondence in quantum gravity (…

In joint work with Kannan Soundararajan, we consider the behavior of random multiplicative functions when summed over subsets of the integers in [1, N], and give several examples of sets where such sums satisfy a central limit theorem. In contrast, as we know from…

In this lecture, we present a new method to solve the scattering problem defined by two planar, rectangular, semi-infinite open wave guides that meet along a common perpendicular line. We use the method of fundamental solutions to reduce the scattering problem to a system of Fredholm integral…