# Department Colloquium

Organizers: Mohammed Abouzaid, Amir Dembo (Fall & Winter Quarters), and Kannan Soundararajan (Spring Quarter)

## Past Events

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…

The problem of finding the smallest eigenvalue of a Hermitian matrix (also called the ground state energy) has wide applications in quantum physics. In this talk, I will first briefly introduce the mathematical setup of quantum algorithms, and discuss how to use textbook quantum algorithms to…

In the last few years there has been an explosion of new results about surfaces in 4-space. In this talk, we will start by discussing various kinds of surfaces and some basic questions about them, like what it means for two of them to be the equivalent. We will then discuss two ways to describe…

Some of the most important problems in combinatorial number theory ask for the size of the largest subset of the integers in an interval lacking points in a fixed arithmetically defined pattern. One example of such a problem is to prove the best possible bounds in Szemer\'edi's theorem on…