## Department Colloquium

### Friday, October 18th, 2019

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Jeremy Quastel (University of Toronto)

**Title:** The KPZ fixed point.

**Abstract: ** The one dimensional KPZ universality class contains random growth models, directed random polymers, stochastic Hamilton-Jacobi equations (e.g.~the eponymous Kardar--Parisi--Zhang equation). It is characterized by unusual scale of fluctuations, some of which appeared earlier in random matrix theory, and which depend on the initial data, the explanation being that on large scales everything approaches a special scaling invariant Markov process, the KPZ fixed point, which turns out to be a new type of integrable system, leading to unexpected connections between probability and dispersive partial differential equations.

**Prof. Jeremy Quastel** specializes in probability theory, stochastic processes and partial differential equations. He obtained is Ph.D.~from the Courant Institute at NYU. He was a postdoctoral fellow at the MSRI in Berkeley, then was a faculty at UC-Davis until he returned to Canada in 1998, where he is now a professor at the University of Toronto and the current chair of the Mathematics department.

Among his accolades, Prof. Quastel received a Sloan Fellowship in 1996, was an invited speaker at the ICM in 2010, gave the Current Developments in Mathematics 2011 and St. Flour 2012 lectures, and was a plenary speaker at the International Congress of Mathematical Physics in Aalborg 2012. He is a fellow of the Royal Society of Canada.