Robert Buckingham (U. Cincinnati)

Universality in Mathematical Physics

A major goal of modern analysis is to show when seemingly unrelated objects behave the same under an appropriate limit.  For example, the height of pine trees and the life span of bears in a forest can both be reasonably modeled by normal distributions.  In the past fifteen years a broad array of physical phenomena ranging from bus arrival times to crystal growth models have been shown to exhibit universal behavior.  We will give a brief overview of many of these recent results, focusing on one problem from probability (eigenvalues of the small-rank external source random matrix model) and one problem from differential equations (asymptotic behavior of the semiclassical limit of the sine-Gordon equation).  We will also show that many of the same mathematical tools can be used to study both problems.

Apr 1 at 4pm in Geo/Phys Room 407