# Video Lectures

A finite set system is union-closed if for every pair of sets in the system their union is also in the system. Frankl in 1979 conjectured that for any such system there exists an element which is contained in ½ of the sets in that system (the only...

Given a convex billiard table, one defines the set swept by locally maximizing orbits for convex billiard. This is a remarkable closed invariant set which does not depend (under certain assumptions) on the choice of the generating function. I shall...

Discrepancy theory provides a powerful approach to improve upon the bounds obtained by a basic application of the probabilistic method. In recent years, several algorithmic approaches have been developed for various classical results in the area. In...

P-adic non abelian Hodge theory, also known as the p-adic Simpson correspondence, aims at describing p-adic local systems on a smooth rigid analytic variety in terms of Higgs bundles. I will explain in this talk why the « Hodge-Tate stacks » recently...

A Lagrangian cobordism between Legendrian knots is an important notion in symplectic geometry. Many questions, including basic structural questions about these surfaces are yet unanswered. For instance, while it is known that these cobordisms form a...

Matrix powering, and more generally iterated matrix multiplication, is a fundamental linear algebraic primitive with myriad applications in computer science. Of particular interest is the problem’s space complexity as it constitutes the main route...

While conducting a series of number-theoretic machine learning experiments, He, Lee, Oliver, and Pozdnyakov noticed a curious oscillation in the averages of Frobenius traces of elliptic curves over Q. If one computes the average value of a_p(E) for...

Suppose that Σ⊂ℂ is compact and symmetric about the real axis and is a finite union of rectangles and real intervals with transfinite diameter dΣ greater than 1. Suppose that μ is a H older arithmetic probability distribution on Σ defined in our work...

I will describe the construction of a global Kuranishi chart for moduli spaces of stable pseudoholomorphic maps of any genus and explain how this allows for a straightforward definition of GW invariants. For those not convinced of its usefulness, I...

The formula introduced by Robert Lipshitz for Heegaard Floer homology is now one of the basic tools for those working with HF homology. The convenience of the formula is due to its combinatorial nature. In the talk, we will discuss the recent...