Mahler Lecture Tour 2018

Date & Time: Thursday 8 November; 15:00–16:00
Venue: Horace Lamb Lecture Theatre, Univ. Adelaide
Speaker: Ivan Corwin (Columbia Univ., USA)

Hosted by the The School of Mathematical Sciences, The University of Adelaide.

Title: Diffusion in random media

Abstract

In 1827 the botanist Robert Brown observed the seemingly irregular motion of pollen immersed in water. A mathematical model for this Brownian motion was proposed later by Einstein in 1905. Since then, it is well validated that motion in quickly mixing random media is well modeled by Brownian motion. In this talk we consider what happens when many particles are released in the same media. Do they behave like independent Brownian motions or does their common environment affect their collective behavior? We will see that the extreme value statistics (i.e., largest displacement) is heavily influenced by the random media and in a one-dimensional model, relying upon some surprising exact solvability techniques from quantum integrable systems, we will relate these statistics to random matrix theory and the Kardar–Parisi–Zhang universality class for random growth models.
Absolutely no background is required or expected for this talk.

Biography

Corwin received his Ph.D. from the Courant Institute in 2011 and has since held positions at Microsoft Research, MIT, Institute Henri Poincaré, and now Columbia. He was a Clay Research Fellow and is presently a Packard Fellow, and a Fellow of the Institute of Mathematical Statistics. He was the recipient of the Alexanderson Award, Rollo Davidson Prize, Young Scientist Prize of the IUPAP, and gave an invited lecture at the 2014 ICM.

supported by AMSI.