Previous Conferences & Workshops

Every area-minimizing hypercone having only an isolated singularity fits into a foliation by smooth, area-minimizing hypersurfaces asymptotic to the cone itself. In this talk I will present the following epsilon-regularity result: every minimal...

Courant's theorem states that the k-th eigenfunction of the Laplace operator on a closed Riemannian manifold has at most k nodal domains. Given a ball of radius r, we will discuss how many of nodal domains can intersect a ball (depending on r and k)...

Optimal transport has been used to have new insights on a variety of mathematical questions, ranging from functional inequalities to economics. We will discuss some of the unexpected uses of optimal transport, as a simple proof of the isoperimetric...

In this talk I will describe joint work with D. Alonso-Orán and A. Córdoba where we extend a result, proved independently by Kiselev-Nazarov-Volberg and Caffarelli-Vasseur, for the critical dissipative SQG equation on a two dimensional sphere. The...

We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional quasi-contact case...

In this talk, I will give two vignettes on the theme of sparse matrices in sparse analysis. The first vignette covers work from compressive sensing in which we want to design sparse matrices (i.e., matrices with few non-zero entries) that we use to...

A (k,m)-Furstenberg set K in F^n, where F is a finite field, is a set such that any k-dimensional subspace of F^n can be shifted so that it intersects K in at least m points. Such sets generalize in a natural way finite field Kakeya sets (in which k...

Some 25 years ago, as announced at a previous version of this seminar, Vaughan and the speaker obtained asymptotic upper and lower bounds for the number of non-trivial integral points on the Segre cubic x31+...+x36=x1+...+x6=0x_1^3+...+x_6^3=x_1+...