Stochastic averaging goes back to Khasminskii in the 1960's. The
standard result is that, given a separation of scales, one can find effective dynamics
for slow components. We investigate the motion of two particles in such a system, in
particular in a randomly-perturbed twist map. The nub of the issue
is how two points escape from a 1-1 resonance zone. Results of Pinsky
and Wihstutz indicate that there is a third scale at work, which we can use to study
the escape from resonance.

The theory of unitary representations originated in the past century as a natural evolution of classical Fourier analysis. In spite of the extremely significant contributions made by Langlands, Harish-Chandra and many other mathematicians, the problem of finding \emph{all} the unitary irreducible representations of a real reductive group remains a challenge: to this day, a complete answer is only known for a handful of groups. In this talk, I will describe some recent progress in the field.