Moduli spaces have many non-trivial connections to other areas of mathematics: combinatorics, dynamics, integrable systems and Poisson geometry, to name a few. Among most celebrated results over the last 30 years one can mention several proofs of Witten’s conjecture about intersection numbers of ψ-classes (Kontsevich, Mirzakhani and others), computation of Euler’s characteristics of moduli spaces (Harer-Zagier), development of the higher Teichmüller theory (Fock, Goncharov) and its links with cluster algebras and associated Poisson structures (Fomin, Zelevinsky).
The research problems central for the program are:
|Amol Aggarwal, Harvard University||Nicolai Reshetikhin, University of California,|
|Anton Alekseev, University of Geneva||Berkeley Michael Shapiro, Michigan State University|
|Gaëtan Borot, Max Planck Institute for Mathematics||Leon Takhtajan, Stony Brook University and EIMI|
|Vladimir Fock, University of Strasbourg||Richard Wentworth, University of Maryland|
|Sergey Fomin, University of Michigan||Don Zagier, Max Planck Institute for Mathematics|
|Martin Möller, Goethe University||Anton Zorich, Skoltech and IMJ – PRG|
|Alexey Rosly, Skoltech||Dimitri Zvonkine (CNRS) (to be confirmed)|
The program is supported by a grant from the Government of the Russian Federation, agreements 075-15-2019-1619 and 075-15-2019-1620, and by a grant from Simons Foundation.