I appreciate there's not much on here yet, but hey, I'm only a year into my PhD!
I'm doing my PhD with Dr Perla Sousi. Currently, we are looking at the mixing time of a random walk on dynamical percolation where the underlying graph is the complete graph. For the moment, we are looking at the annealed mixing time of the walk: we consider the worst-case initial environment and starting location for the walk, then look at the TV distance of the walk from uniform while averaging over the environment.
My email address is firstname.lastname@example.org.