Analytic techniques in Dynamics and Geometry

May 28, 2023, 7:00 PM – Jun 2, 2023, 2:00 PM

SwissMAP Research Station Les Diablerets Switzerland

Organized by Mihajlo Cekic (University of Zurich), Artur Avila (University of Zurich), Thibault Lefeuvre (Sorbonne University)

This workshop aims at bringing together mathematicians making use of analytic methods in their study of dynamics, geometry, PDEs, or inverse problems.

In the past twenty years, microlocal and functional analysis techniques have encountered a large success both in hyperbolic dynamics and geometry as they turned out to be ripe enough to tackle unsolved problems in these areas. This development was followed by a number of spectacular results and, on one hand, this workshop aims to celebrate the success of such methods by bringing together the leading specialists. On the other hand, its goal is to serve as a fertile environment for the advancement of analytic methods in more complicated dynamical systems, such as partially hyperbolic or parabolic, by gathering the pioneers in these areas at one place and spurring a novel exchange of ideas between experts in analysis and dynamics. Topics should include:

• the theory of Pollicott-Ruelle resonances and transfer operators in hyperbolic dynamics;

• analytic methods in non-hyperbolic dynamics (frame and horocycle flows, for instance);

• geometric inverse problems;

• scattering resonances, spectral rigidity, quantum ergodicity, or semiclassical phenomena.