Department Colloquium

Random surfaces are central paradigms in equilibrium statistical mechanics. As these surfaces become larger, their statistical behaviors become strongly dependent on how their boundaries are pinned down. This can lead to phase transitions, such as facet edges separating a flat region of the…

A major goal of additive combinatorics is to understand the structures of subsets A of an abelian group G which has a small doubling K = |A+A|/|A|. Freiman's celebrated theorem first provided a structural characterization of sets with small doubling over the integers, and subsequently Ruzsa in…

The moduli space M_g of genus g curves (or Riemann surfaces) is a central object of study in algebraic geometry. Its cohomology is important in many fields. For example, the cohomology of M_g is the same as the cohomology of the mapping class group, and is also related to spaces of modular forms…

Determining the structure of the equations of an algebraic curve in its canonical embedding (given by its holomorphic forms) has been a central question in algebraic geometry from the beginning of the subject. In 1984 Mark Green put forward a very elegant conjecture linking the complexity of the…

The world teems with examples of invasion, in which one steady state spatially invades another. Invasion can even display a universal character: fine details recur in seemingly unrelated systems. Reaction-diffusion equations provide a mathematical framework for these phenomena. In this talk…

Abstract: 

Harmonic measure is the probability that a Brownian traveler starting from the center of the domain exists through a particular portion of the boundary. It is a fundamental concept at the intersection of PDEs, probability, harmonic analysis, and geometric measure theory,…

In the study of fluid dynamics, turbulence poses a significant challenge in predicting fluid behavior, and it remains a mystery for mathematicians and physicists alike. Recently, there has been some exciting progress in our understanding of ideal turbulence: starting from Onsager’s theorem…

A striking phenomenon in probability theory is universality, where different probabilistic models produce the same large-scale or long-time limit. One example is the Kardar-Parisi-Zhang (KPZ) universality class, which contains a wide range of natural models, including growth processes modeling…

"...in this field, almost everything is already discovered, and all that remains is to fill a few unimportant holes."  - Philipp von Jolly in his recommendation to Max Planck not to go into physics.

Since 2015 I am taking part in a long project (more precisely, a series of projects)…

This talk will be a guided tour of some very distinct, but highly interconnected areas of combinatorics, algebraic geometry and number theory. 

Graph complexes were introduced by Kontsevich and encode the contraction of edges in a graph. Despite the elementary definition, their…