Genet-Roussel Seminarorganized by Carlos Grossi & Igor Mencattini
|Third Genet-Roussel Geometry Day|
13/11/2017 at 10h30 - Auditório Fernăo Stella, ICMC - 6001
Misha Verbitsky (IMPA). Torelli theorem for hyperkaehler manifolds
Abstract: I will explain how one solves the moduli problem for holomorphically symplectic manifolds.
Volodya Roubtsov (Angers). New decorated character varieties and Painlevé equations
Abstract: We propose an another version of "wild" character varieties related to irregular connections on Riemann surfaces and study various types of Poisson structures on it. Connection with cluster structures are discussed. We propose a new version of a "wild" Riemann-Hilbert correspondence in this framework. We argue (if I have time) that the corresponded quantum objects are subjected to a Fock-Rosly type algebra.
My talk is based on joint works (partially in progress) with Leonya Chekhov (Moscow-East Lancing) and Marta Mazzocco (Loughborough).
14/11/2017 at 14h00 - Auditório Luiz Antonio Favaro, ICMC - 4111
This edition of the Genet-Roussel Seminar will consist of two consecutive talks (with coffee break).
Misha Verbitsky (IMPA). Ergodic theory for the mapping group action on geometric structures I, II
Abstract: The Teichmuller space of geometric structures of certain type is the quotient of the set of all geometric structures of this type by the group of isotopies (that is, the connected component of the diffeomorphism group). The natural examples are Teichmuller spaces of complex, symplectic, holomorphically symplectic, hyperkahler or holonomy G2 structures; they are all finite-dimensional and often smooth manifolds. I will focus on the Teichmuller space of symplectic structures, which is a smooth, finite-dimensional manifold, and describe it explicitly for hyperkahler manifolds, such as K3 surface and a torus. I will explain the ergodic properties of the mapping group action on the symplectic Teichmuller space, and give some applications.