Past Events
A perfect difference set is a set S of residues modulo v such that every nonzero residue can be uniquely represented as a difference of two elements of S. In 1980, Erdős offered $1000 for determining whether any set of integers that doesn't already repeat a difference can be extended to a…
The concept of $p$-curvature originated in Grothendieck's unpublished work from the 1960s and was subsequently developed further by V. Katz. The $p$-curvature plays an important role in the theory of ordinary differential equations (ODEs) as well as holonomic PDEs, establishing a connection…
In this talk, I will focus on simultaneous non-vanishing results for Dirichlet L-functions at the central point 1/2. Specifically, I will describe how to obtain a positive proportion of simultaneous non-vanishing result for four L-functions as we vary over characters \chi modulo q,…
We use Floer homology to study some more exotic constructions in four-dimensions. This is joint work with Lisa Piccirillo
The Euler-Poisson system of partial differential equations describes the dynamics of a self-gravitating gas. For the energy-critical polytropic pressure law, there is an explicit steady-state solution describing an isolated star. I will discuss recent work which describes the nonlinear phase…
Abstract
The authors study the problem of stability of the catenoid, which is an asymptotically flat rotationally symmetric minimal surface in Euclidean space, viewed as a stationary solution to the hyperbolic vanishing mean curvature equation in Minkowski space. The latter is a…
We will continue our study of localization schemes and related topics.
Graphs with optimally large spectral gap are known as Ramanujan graphs. Previous constructions of Ramanujan graphs are based on number theory and have specific constraints on the degree and number of vertices. In this talk, we show that, in fact, most regular graphs are…
The bridge principle is the idea that you can join compact minimal submanifolds along their boundaries to produce an “approximately minimal” submanifold, called the approximate solution, and apply a small normal perturbation to make the new configuration minimal. It dates back to Lévy (1948…