# Department Colloquium

Organizers: Rafe Mazzeo & Ravi Vakil

## Upcoming Events

Abstract

## Past Events

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…

In the world of homotopy theory, there are analogs of abelian groups called Spectra. Spectra are extremely useful in algebraic topology, differential topology, algebraic K-theory, and more. According to the primary decomposition theorem, Abelian groups decompose into parts according…

In 1952 R.H. Bing published wild involution (it is an orientation-reversing homeomorphism which squares to the identity) of the three sphere, S^3. This example started a revolution in decomposition space theory which led to the solutions of the double-suspension problem (Edwards and Cannon…

Let T be a subset of R^d, such as a ball, a cube or a cylinder, and consider all possibilities for packing translates of T, perhaps with its rotations, in some bounded domain in R^d. What does a typical packing of this sort look like? One mathematical formalization of this question is to fix the…