# Past Events

This talk plans to design an immersive game for people who are still kids at heart to experience learning mathematics from the very beginning, but in a completely non-traditional way. We will start analysis without \epsilon-\delta, start algebra without writing operators and laws, start topology…

Consider a quadratic polynomial Q(x_1,...,x_n) of a random binary sequence (x_1,...,x_n). To what extent can Q(x_1,...,x_n) concentrate on a single value? This is a quadratic version of the classical Littlewood-Offord problem; it was was popularised by Costello, Tao and Vu in their study of…

Abstract

Is there a partition of the natural numbers into finitely many pieces, none of which contains a Pythagorean triple (i.e. a solution to the equation x^2+y^2=z^2)? This is one of the simplest questions in arithmetic Ramsey theory which is still open. I will present a recent partial result, showing…

Curve graphs are crucial tools for studying mapping class groups of surfaces. However, many basic questions on their geometry remain open. In this talk, we will shed light on the geometry of curve graphs by describing “filtrations” of them by hyperbolic graphs. These filtrations yield quasi-…

Abstract: In this talk, I will present a method to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. We first present a conditional result. Assuming that a global solution to the geometric reduced system exists and satisfies several well-chosen…

I will discuss joint work with Luya Wang on the other direction of the Donaldson 4-6 problem. Specifically, we show that any two simply-connected symplectic 4-manifolds, whose products with S^2 are deformation equivalent, have the same Gromov-Witten invariants. The proof relies on a…

I will talk about parallelization of sampling algorithms. The main focus of the talk will be a new result, where we show how to speed up sampling from an arbitrary distribution on a product space [q]^n, given oracle access to conditional marginals. Our algorithm takes roughly n^{2/3} polylog(n,…

Scholze has conjectured the existence of the so-called Igusa stacks, which have close relation to Shimura varieties. In my thesis and the joint work in progress with Daniels, van Hoften and Kim, these conjectural stacks are constructed for many interesting classes of Shimura varieties. In this…