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Mathematics Colloquium

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Date:  Monday, May 02, 2016

Title:  GL(2,R) invariant subvarieties of the Hodge bundle

Abstract:  I will discuss the GL(2,R) action on the moduli space of translation surfaces, starting from its roots in the 80s in the study of the Teichmuller metric and the study of billiards in polygons. I will discuss joint work with Alex Eskin, Curtis McMullen, and Ronen Mukamel, giving six new GL(2,R) invariant subvarieties of the Hodge bundle, three of which give rise to totally geodesic subvarieties of the moduli spaces of Riemann surfaces. These varieties are related to certain Hurwitz spaces of covers of P^1 and to real multiplication of Hecke type on Jacobians of Riemann surfaces. I will also discuss joint work with Maryam Mirzkhani, which uses a combination of algebraic geometry, dynamics, and flat geometry to compute GL(2,R) orbit closures associated to triangles.


Speaker:  Alex Wright
Institution:  Stanford University

 

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