# Video Lectures

A famous conjecture of Littlewood states that the Fourier transform of every set of N integers has l^1 norm at least log(N), up to a constant multiplicative factor. This was proved independently by McGehee-Pigno-Smith and Konyagin in the 1980s. This...

Humans have been thinking about polynomial equations over the integers, or over the rational numbers, for many years. Despite this, their secrets are tightly locked up and it is hard to know what to expect, even in simple looking cases. In this talk...

Monte Carlo simulation is a powerful tool to study the Euclidean path integral. In the context of gauge/gravity duality, it enables us to access the strong-coupling regime of the QFT side. In this talk, we provide the latest results of the...

A meandric system of size $n$ is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on $\{1,\dots,2n\}$, one drawn above the real line and the other below the real line. Equivalently, a meandric system is a coupled...

A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of the alternating group An be?

In the talk we will completely solve the problem by...

Approximate lattices in locally compact groups are approximate subgroups that are discrete and have finite co-volume. They provide natural examples of objects at the intersection of algebraic groups, ergodic theory and additive combinatorics... with...

Work of Mark Shusterman and myself has proven an analogue of Chowla's conjecture for polynomial rings over finite fields, which controls k-points correlations of the Möbius function for k bounded by a certain function of the finite field size...

Persistence modules and barcodes are used in symplectic topology to define new invariants of Hamiltonian diffeomorphisms, however methods that explicitly calculate these barcodes are often unclear. In this talk I will define one such invariant...

### A Correspondence Between Obstructions and Constructions for Staircases in Hirzebruch Surface

The ellipsoidal embedding function of a symplectic four manifold M measures how much the symplectic form on M must be dilated in order for it to admit an embedded ellipsoid of some eccentricity. It generalizes the Gromov width and ball packing...

The spectral norm provides a lower bound to the Hofer norm. It is thus natural to ask whether the diameter of the spectral norm is finite or not. During this short talk, I will give a sketch of the proof that, in the case of Liouville domains, the...