Video Lectures

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...

In this talk, we explore new techniques to probe the analytic structure of scattering amplitudes in perturbative Quantum Field Theory. The goal of this approach is to leverage symmetries, limits, and analyticity in order to circumvent the explicit...

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...

We consider the standard L-function attached to a cuspidal automorphic representation of a general linear group. We present a proof of a subconvex bound in the t-aspect. More generally, we address the spectral aspect in the case of uniform parameter...

Recent radio observations of inflowing and outflowing plasma in the vicinity of supermassive black holes are linked to simple phenomenological models via general relativistic magnetohydrodynamic simulations through a methodology called "Observing"...