Microlocal analysis exploits mathematical manifestations of the classical/quantum (particle/wave) correspondence and has been a successful tool in spectral theory and partial differential equations. We can say that these last two fields lie on the quantum/wave side.

Recently, microlocal methods have been applied to the study of classical dynamical problems, in particular of chaotic (Anosov) flows. I will illustrate this by proving that the order of vanishing of the dynamical zeta function at zero for negatively curved surfaces is given by the absolute value of the Euler characteristic (joint work with S Dyatlov).

https://mediaspace.gatech.edu/media/zworski/1_erjjl4mr