Room P3.10, Mathematics Building

Brian Hall

Brian Hall, Notre Dame University
Heat equation and Segal-Bargmann transform on unitary groups in the large-$N$ limit

I will discuss the heat equation on the unitary group $U(N)$ in the limit as $N$ tends to infinity, with an eye toward study of the Segal-Bargmann transform. On certain classes of functions on $U(N)$, the Laplacian greatly simplifies as $N$ gets large. Indeed, the large-$N$ limit of the Laplacian satisfies a first-order product rule, meaning that the cross terms in the usual product rule for the Laplacian become negligible. As a result, we are able to obtain a limiting Segal-Bargmann transform on this class of functions. These results are joint work with Bruce Driver and Todd Kemp and were motivated by earlier work of Philippe Bianne.

Additional file

document preview