SFU Mathematics of Computation, Application and Data ("MOCAD") Seminar: Denis Grebenkov

In this overview talk, I will present the encounter-based approach to diffusive processes in Euclidean domains and highlight its fundamental relation to the Steklov spectral problem. So, the Steklov eigenfunctions turn out to be particularly useful for representing heat kernels with Robin boundary condition and disentangling diffusive dynamics from reaction events on the boundary. I will also discuss applications of this approach in physical chemistry (to describe diffusion-controlled reactions) and in statistical physics (to determine the statistics of encounters and various first-passage times). Some open questions related to spectral, probabilistic and numerical aspects of this spectral problem will be outlined.