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...

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...

Knots associated to overtwisted manifolds are less explored. There are two types of knots in an overtwisted manifold – loose and non-loose. Non-loose knots are knots with tight complements whereas loose knots have overtwisted complements. While we...

In this talk we consider the links of simple singularities, which are contactomoprhic to S3/G for finite subgroups G of SU(2,C). We explain how to compute the cylindrical contact homology of S3/G by means of perturbing the canonical contact form by...

Recent years have seen the appearance of a plethora of possible metrics on spaces of Lagrangian submanifolds. Indeed, on top of the better-known Lagrangian Hofer metric and spectral norm, Biran, Cornea, and Shelukhin have constructed families of so...