Previous Conferences & Workshops

The set of positive integer points of the celebrated Markov surface admits the structure of a 3-regular tree. My objective in this talk is to unveil a similar phenomenon for Mordell-Schinzel surfaces; namely that the set of positive integer points...

Since the work of Jacobi and Siegel, it is well known that Theta series of quadratic lattices produce modular forms. In a vast generalization, Kudla and Millson have proved that the generating series of special cycles in orthogonal and unitary...

In a recent collaboration with a group of algebraic combinatorists at ICERM, we came across a rather surprising set of permutations, which (in a natural sense I'll explain in the talk) form an unexpectedly gigantic hypercube.  This set of...

There has been considerable activity in establishing effective versions of equidistribution theorems in homogeneous dynamics in recent years. In this talk, we report on new results concerning effective equidistribution for one-parameter unipotent...

We exhibit a new class of self-similar implosion solutions for the full compressible Euler equations. For any value of the adiabatic exponent, we construct a sequence of implosion profiles that are smooth before collapse and have an explicit...

We propose an extension of Yao's standard two-party communication model, where Alice and Bob respectively hold probability distributions p and q over inputs to a function f, rather than singleton inputs. Their goal is to estimate E[f(x,y)] to within...

Let $X/S$ be a regular scheme over the spectrum of a discrete valuation ring. Bloch conjectured a formula relating algebraic differential forms to the total dimension of the vanishing cohomology of $X/S$. In this talk, I will explain a proof of this...

In probability theory, universality is the phenomenon where random processes converge to a common limit despite microscopic differences. For instance, the random walk, under mild conditions, converges to the same Brownian motion seen from afar...

In this talk, I will discuss the solution to several problems in two closely related settings: set families in 2^[n] with many disjoint pairs, and low-rank matrices with many zero entries.

Highlights include a resolution of an old question of Daykin...