# Video Lectures

We study CM cycles on Kuga-Sato varieties over X(N) via theta lifting and relative trace formula. Our first result is the modularity of CM cycles, in the sense that the Hecke modules they generate are semisimple whose irreducible components are...

In this talk I will discuss two undetected populations of black holes. In the faraway Universe, the first lensed z > 6 quasar (J0439+1634) was recently discovered. We predicted that the observed population of quasars should contain many mildly...

I'll describe a method for analyzing the first-order theory of an arithmetic group using its congruence quotients. When this method works, it gives a strong form of first-order rigidity together with a complete description of the collection of...

The query model is one of the most basic computational models. In contrast to the Turing machine model, fundamental questions regarding the power of randomness and quantum computing are relatively well-understood. For example, it is well-known...

We will discuss the first steps in an approach to proving homological mirror symmetry for Looijenga pairs through tropical Lagrangian sections. Namely, we will see how to construct these Lagrangian sections from tropical data corresponding to line...

The honest answer to the question is that I actually do not know. I will therefore rather talk about several famous examples that are widely called "h-principle results" and try to explain some of the ideas behind the ones I am most familiar with.

...We consider the problem of computing a Gradient Descent solution of a continuously differentiable function f on a bounded convex domain, i.e., finding a "point where Gradient Descent terminates". Equivalently, this corresponds to computing a so...