Video Lectures

I will discuss work in progress with Morgan Weiler on knot filtered embedded contact homology (ECH) of open book decompositions of S^3 along T(2,q) torus knots to deduce information about the dynamics of symplectomorphisms of the genus (q-1)/2 pages...

Behaviors of objects of algebraic interest, such as polynomials, elliptic curves and number fields -- many of which are still unknown -- fall into the field of arithmetic statistics..  By bringing in Fourier analysis to interplay with a wide variety...

We discuss some consequences of the existence of a Siegel zero for various questions relating to the distribution of the prime numbers, and in particular to conjectures of Hardy-Littlewood and Chowla type.  This is joint work with Joni Teravainen.

Abstract: Low-lying horocycles are known to equidistribute on the modular curve. Here we consider the joint distribution of two low-lying horocycles of different speeds in the product of two modular curves and show equidistribution under certain...

This is a joint work with Reza Gheissari (Northwestern) and Aukosh Jagannath (Waterloo), Outstanding paper award at NeurIPS 2022. We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime...

Lagrangian Floer theory is a useful tool for studying the structure of the homology of Lagrangian submanifolds. In some cases, it can be used to detect more- we show it can detect the framed bordism class of certain Lagrangians and in particular...

I discuss the spectral and arithmetic side of the relative trace formula of Kuznetsov type for congruence subgroups of SL(n, Z) with applications to automorphic density theorems. A particular focus is on properties of general Kloosterman sums as...

This talk will be about a ferromagnetic spin system called the Blume-Capel model. It was introduced in the '60s to model an exotic multi-critical phase transition observed in the magnetisation of uranium oxide. Mathematically speaking, the model can...

The last decade has witnessed a revolution in the circle of problems concerned with proving sharp moment inequalities for exponential sums on tori. This has in turn led to a better understanding of pointwise estimates, but this topic remains...

Robust sublinear expansion represents a fairly weak notion of graph expansion which still retains a number of useful properties of the classical notion. The general idea behind it has been introduced by Komlós and Szemerédi around 25 years ago and...