Dynamics: Topology and Numbers

Trimester Program

January 6 - April 24, 2020

Organizers: Manfred Einsiedler, Martin Möller, Anke Pohl, Tom Ward

The program centers around modern aspects of dynamical systems, with dynamics on homogeneous spaces as the core topic. Interactions with Teichmüller dynamics, Diophantine approximation and quantum chaos are the main themes of the planned activities. The classification of ergodic invariant measures and orbit closures of higher rank actions on homogeneous spaces is still far from complete. Results in this area find application to equidistribution phenomena and Diophantine problems of many sorts. Active areas of current research include higher rank diagonalizable flows, the horocycle flow and the SL2(R)-action on flat surfaces, quantum unique ergodicity, and links to other parts of number theory including the theory of automorphic forms. 

We will host long-term visitors and plan the following focussed activities:

  • Winter School on dynamics, topology and numbers (January 13-17)
  • Conference: Transfer operators in number theory and quantum chaos (February 3-7)
  • Conference: Dynamics on homogeneous spaces (March 16-20)
  • Conference: Dynamics on flat surfaces and their moduli spaces (April 20-24 )

Those planning to participate include:
Jayadev Athreya, Uri Bader, Yves Benoist, Jon Chaika, Alex Eskin, Elena Fuchs, Alex Kontorovich, Jens Marklof, Amir Mohammadi, Hee Oh, Dierk Schleicher, Uri Shapira, Lior Silberman, Barak Weiss, Anton Zorich