# Past Events

This talk discusses the unstructured sparse recovery problems of a general form. The task is to recover the spike locations and weights of an unknown sparse signal from a collection of its unstructured observations. Examples include rational approximation, spectral function estimation, Fourier…

Given n points and a smooth Jordan curve in the complex plane, what is the minimum degree of a non-constant polynomial which maps all of the points to the curve? It is easy to bound the degree above by n-1, while if the points are collinear and the curve is an ellipse, then the degree is…

Abstract: In this work we prove global well-posedness for the massive Maxwell-Dirac equation in the Lorentz gauge in $\mathbb{R}^{1+3}$, for small and localized initial data, as well as modified scattering for the solutions. In doing so, we heuristically exploit the close connection…

Given a nondegenerate smooth variety X in P^n, let S(X) (resp. T(X)) be the subvariety of the Grassmannian Gr(2, n+1) consisting of secant (resp. tangent) lines to X. I will give closed-form formulae for the classes of S(X) and T(X) in the Chow ring of Gr(2,n+1) in terms of the “higher…

Generating families (generating functions) for exact Lagrangian or Legendrian submanifolds provides a finite dimensional approach to understanding nonclassical invariants of the submanifolds. Given an exact Lagrangian cobordism between Legendrians in 1-jet bundles, we prove that a generating…

We will discuss non-Hermitian random matrix models, namely the universality problem for local eigenvalue statistics. The main result is universality in the bulk (i.e., away from the edge of the limiting spectrum) for complex eigenvalues of real non-symmetric matrices with i.i.d. entries. The…

The classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can consider a complementary perspective - given a smooth projective variety whose nonrationality is known, how "irrational" is it? I will survey…

In this talk, I will continue to describe aspects of geometric optics, one of the main themes introduced earlier. I also hope to describe a bit more about how this relates to some interesting properties of hyperbolic PDE. In particular, I hope to motivate a bit more about why you may…

Automorphy lifting theorems establish situations in which Galois representations over \bar{Q_p} are automorphic if their residual representation has an automorphic lift. In 2018, Allen et. al. proved the first automorphy lifting theorem for n-dimensional Galois representations over a CM field…

An “abstract polyhedron” means, roughly, a graph that “might be the edges and vertices of a polyhedron”. When can we promote “might be” to “is”? This question is answered by a beautiful theorem about circle packings on the sphere. I will explain the proof of this theorem, as well as some…