Institute of Mathematics

Talk

Modul:   MAT075  Zurich Graduate Colloquium

What is... measure rigidity?

Emilio Corso talk

Date: 03.12.19  Time: 17.15 - 18.30  Room:

In an influential paper published in 1967, Furstenberg marked the outset of the study of rigidity properties for invariant measures arising in algebraically-defined dynamical systems. His conjectures and achievements prompted intensive research activity, purporting to understand the manifestation of similar rigidity phenomena in ever more general contexts. Recent developments along this line of investigation turned out to be paramount for the (complete or partial) resolution of long-standing conjectures pertaining to Hilbert's eleventh problem, Diophantine approximation, equidistribution of Hecke-Maass forms and the kinematics of high-energy quantum particles, statistical properties of the Lorentz gas with quasicrystal scatterer configurations. I will survey some of these applications, hopefully shedding some light on how measure rigidity comes into play.