Tom Haines (University of Maryland)
Smoothness of Schubert varieties in twisted affine Grassmannians

Abstract: This talk will describe results about Schubert varieties in affine Grassmannians. In joint work, Timo Richarz and I gave a complete list of smooth (resp. rationally smooth) Schubert varieties in the twisted affine Grassmannian associated with a tamely ramified group and a special vertex of its Bruhat-Tits building. When the underlying group is not split, there are surprising cases of smoothness not occurring in the split group setting, called cases of *exotic smoothness*. This is closely related to the recent He-Pappas-Rapoport classification of Shimura varieties with good reduction, and to the cases of *exotic good reduction* they describe. Our classification of smooth Schubert varieties verifies a conjectural classification postulated by Rapoport in 2010. The proof uses our theorem on normality of such Schubert varieties, a result which generalizes earlier work of Faltings and Pappas-Rapoport.