Here is the video of a talk I gave on Thursday, August 31, at the joint Melbourne Universities Probability seminar. The abstract of the talk is the following

We study the Brownian motion on the non-compact Grassmann manifold U(n−k,k)/U(n−k)U(k) and some of its functionals. The key point is to realize this Brownian motion as a matrix diffusion process, use matrix stochastic calculus and take advantage of the hyperbolic Stiefel fibration to study a functional that can be understood in that setting as a generalized stochastic area process. In particular, a connection to the generalized Maass Laplacian of the complex hyperbolic space is presented and applications to the study of Brownian windings in the Lie group U(n−k,k) are then given. This is a joint work with Nizar Demni and Jing Wang.