Todd Kemp - University of California, San Diego (UCSD) The group GL(N) of invertible complex matrices is a Lie group; equipped with a left-invariant metric, it acquires a canonical (matrix valued) Brownian motion process. It has a large-N limit known as free multiplicative Brownian motion, which was introduced by Biane in 2001. I proved that it is the large-N limit of the GL(N) Brownian motion, and together with Guillaume Cébron we studied the (Gaussian) fluctuations of this limit. The big question is: what is the large-N limit of the empirical eigenvalue distribution of this Brownian motion? Simulations show it is quite complicated, supported on a domain that is not simply connected for t>4. The limit is (very likely) the Brown measure of gt, which is a fierce object to compute. In this talk, I will describe very recent joint work with Brian Hall: we explicitly compute the support set of the Brown measure of gt, and show that it asymptotically contains the eigenvalues of the Brownian motion on GL(N). In the process, we provide a seemingly new description of the support of the Brown measure of any operator.