Sam Grushevsky : Differentials with real periods and the geometry of the moduli space of curves

Posted by , part of the Algebraic Geometry Seminar.

At

Nov. 14, 2008, 4:30 p.m.

In

SEO 636

Abstract

Motivated by constructions in the Whitham theory (perturbation theory for integrable systems), we consider meromorphic differentials with prescribed singular parts and real periods on Riemann surfaces. We use these differentials to define real-analytic foliations of $M_g$ with complex leaves, and to give a short proof of the Diaz' bound on the dimension of complete subvarieties of $M_g$; potential further applications will also be discussed. No familiarity with integrable systems is assumed. Joint work with Igor Krichever