Abstract: This talk will be about joint work with Eyal Goren about the

structure of Picard modular surfaces at a prime p which is inert in the

underlying quadratic imaginary field. The main tool for studying the bad

reduction of Shimura varieties is the theory of local models (due to de

Jong and Rapoport-Zink). Our results concern global geometric questions

which go beyond the theory of global models. For example, we are able to

count supersingular curves on the Picard surface. We also study certain

foliations in its tangent bundle that have not been studied before, and

lead to new conjectures of "Andre-Oort" type. Some of the results should

generalize to other unitary Shimura varieties, but the talk will focus on

U(2,1).

structure of Picard modular surfaces at a prime p which is inert in the

underlying quadratic imaginary field. The main tool for studying the bad

reduction of Shimura varieties is the theory of local models (due to de

Jong and Rapoport-Zink). Our results concern global geometric questions

which go beyond the theory of global models. For example, we are able to

count supersingular curves on the Picard surface. We also study certain

foliations in its tangent bundle that have not been studied before, and

lead to new conjectures of "Andre-Oort" type. Some of the results should

generalize to other unitary Shimura varieties, but the talk will focus on

U(2,1).

## Date:

Mon, 02/01/2017 - 14:00 to 15:00

## Location:

Ros Building, 70A