29 September 2014 to 3 October 2014
International Center for Theoretical Physics
Europe/Paris timezone

From character varieties to isoperiodic foliations: a transfer principle

30 Sep 2014, 15:30
1h
Adriatico Building, Kastler Lecture Hall (International Center for Theoretical Physics)

Adriatico Building, Kastler Lecture Hall

International Center for Theoretical Physics

Strada Costiera, 11 I - 34151 Trieste Italy

Speaker

Bertrand DEROIN (Paris)

Description

Schiffer variations are surgery operations that takes an abelian differential on a curve to another one with the same periods. Viewed in the moduli space of abelian differentials of a fixed genus g>=2, they draw a complex algebraic foliation of dimension 2g-3, called the isoperiodic foliation. Its transverse structure is modelled on an open set contained in the group of complex periods, on which the mapping class group acts via the symplectic group. We will see that the (rich) dynamical properties of this latter are also satisfied by the isoperiodic foliation: this phenomenon is what we call the transfer principle. The fact that it holds relies on the connectivity of certain moduli spaces of abelian differentials on curves with prescribed periods. This is a work in collaboration with Gabriel Calsamiglia and Stefano Francaviglia.

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