**Date & Time:** Friday, October 24, 2008, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:** On Shimura Curves in the Schottky Locus

**Speaker:** Stefan Kukulies, University of Duisberg-Essen

**Abstract:** We show that a given rational Shimura curve *Y* with strictly maximal Higgs field in the moduli space of *g*-dimensional abelian varieties does not lie in the closure of the Schottky locus for large *g*. We achieve this by using a result of Viehweg and Zuo which says that if *Y* lies in the Schottky locus, then the corresponding family of abelian varieties is isogenous over *Y* to the *g*-fold product of a modular family of elliptic curves. After reducing the situation from the field of complex numbers to a finite field, we will see, combining the Weil and Sato-Tate conjectures, that this is impossible for large genus *g*.