Video Lectures

In the matrix completion problem, we have a matrix $M$ where we are only given a small number of its entries and our goal is to fill in the rest of the entries. While this problem is impossible to solve for general matrices, it can be solved if $M$...

Let $G$ be a compact group and let $f_{ij}\in L_2(G)$ be bandlimited functions. We define the Non-Unique Games (NUG) problem as finding $g_1\ldots,g_n\in G$ to minimize $\sum_{i,j=1}^n f_{ij}(g_i g_j^{-1})$. We devise a relaxation of the NUG problem...

One of the main ideas that comes up in the proof of Fermat's Last Theorem is a way of "counting" 2-dimensional Galois representations over $\mathbb Q$ with certain prescribed properties. We discuss the problem of counting other types of Galois...

Conventional Riemann-Hilbert correspondence relates the category of holonomic $D$-modules (de Rham side) with the category of constructible sheaves (Betti side). I am going to reconsider this relationship from the point of view of deformation...