Past Events

Abstract

In this talk, I will present recent results on the distribution of the maximum of quadratic character sums, as well as some applications. In particular, our work improves results of Montgomery and Vaughan, and gives strong evidence that the Omega result of Bateman and Chowla for quadratic…

About ten years ago, De Lellis and Szekelyhidi made the surprising discovery that Nash’s results on the isometric embedding problem for Riemannian manifolds could be adapted to construct counterintuitive solutions to the Euler equations for incompressible flow. Their work shed new light on…

In the last 20 years there was a huge progress in finding the sharp estimates of weighted singular integrals. This progress was motivated by problems in such various areas as regularity of stochastic processes and borderline regularity of Beltrami equation and certain elliptic…

Z_2-harmonic spinors are singular generalizations of classical harmonic spinors that allow topological twisting around a submanifold of codimension 2 called the singular set. These objects were introduced by Taubes to compactify the moduli spaces of solutions to generalized Seiberg-Witten…

The cohomology groups of moduli spaces of curves are important to several mathematical disciplines, from low-dimensional topology and geometric group theory to stable homotopy theory and quantum algebra. Algebraic geometry endows these groups with additional structures, such as Hodge structures…

The Sylow theorems appear at the very start of group theory. If you look (and we will) you'll see that the proofs are 'just simple combinatorics'. This connection continues. In this talk I'll focus on the Sylow subgroups of the Symmetric group S_n. These have a simple description as 'chandelier…

Motivated by number theoretical results due to Montgomery, 
Hejhal, Rudnick, and Sarnak, we study limiting distribution of k-tuple 
smoothed counting statistics in circular ensembles of random matrices. 
Some of the results were obtained in  collaboration with…

We discuss the problem of distinguishing virtual transverse knots, equivalence classes of virtual braid closures modulo positive stabilization. Some of the most basic conjectures about these objects are surprisingly difficult to answer. We will define some state-sum invariants for virtual…

In the interchange process on a graph $G=(V,E)$, distinguished particles are placed on the vertices of $G$ with independent Poisson clocks on the edges. When the clock of an edge rings, the two particles on the two sides of the edge interchange. In this way, a random permutation $\pi_\beta:V\to…