Beyond the Gaussian Universality Class
Free Public Lecture
Evan Williams Theatre
The bell curve (or Gaussian distribution) is ubiquitous across science, mathematics, statistics and social sciences. It naturally describes variations due to many roughly independent and similarly small random effects. For example, variations in the number of heads in repeated coin flips are described by the bell curve. This "Gaussian universality class" is not all encompassing. For instance, the random variations in the flow of traffic, growth of bacteria on a petri dish, or covariances of large data sets are not well described by the bell curve. In this talk, we will describe how quite surprisingly these three types of systems (plus a few more) all show the same type of variations -- the so called "Kardar–Parisi–Zhang universality class". This talk will be aimed at a very general audience and will feature no equations and lots interesting phenomena, videos and examples.
This lecture is presented by Professor Ivan Corwin, Columbia University, who is this year's AustMS/AMSI Mahler Lecturer.
Professor Ivan Corwin, Columbia University
Professor Ivan Corwin
Ivan Corwin is currently a Professor of Mathematics at Columbia University. His thesis included (in joint work with Amir and Quastel) the exact solution to the Kardar–Parisi–Zhang stochastic partial differential equation. Subsequently, with Borodin, he introduced and developed the theory of Macdonald processes. Along with other collaborators, he has developed the area of Integrable Probability, including the study of stochastic vertex models and the Markov duality approach. He has also worked on discrete approximation theory to stochastic partial differential equations. 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.