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. 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 to describe diffusion-controlled reactions in physical chemistry and the related statistics of first-passage times. Some open questions related to spectral, probabilistic, and numerical aspects of this spectral problem will be outlined.

Refreshments will be served preceding the talk, beginning at 2:45.