The 71st Midwest Partial Differential Equations Seminar May 11-12, 2013 Room TBA East Hall University of Michigan Ann Arbor, MI   Abstract Detail   Title: Large-N limit of the heat equation on unitary groups I will discuss joint work in progress with Bruce Driver and Todd Kemp (both of UCSD), concerning the large-N behavior of the heat equation on the unitary group U(N). Our project builds on earlier work of Ph. Biane and is related to the concept of the "master field" in quantum field theory. Although other work in this area is mostly based on probabilistic methods, our approach is by direct analysis of the Laplacian and heat operator on U(N). A key result is that on certain classes of functions, the Laplacian on U(N) satisfies--in the large-N limit--a Leibniz-type product rule, as if it were a *first-order* operator. Brian Hall University of Notre Dame Email:  bhall@nd.edu Phone: 574-344-3428   BACK to Speaker Listing BACK to Conference Home   Sponsors National Science Foundation, Department of Mathematics at the University of Michigan