Speaker: Prof Yihang Zhu (YMSC)
Title: The Cerednik--Drinfeld uniformization theorem
Time: 14:30-16:00 October 30, 2023 (Monday)
Place: MCM110
Abstract: In this talk we relate the Drinfeld half plane studiedso far in the seminar with certain Shimura curves.which are of more global arithmetic interest. Therelation is expressed in a certain uniformizationtheorem similar to the complex uniformization of theShimura curve by the Poincare half plane. We willdiscuss BC91,IIL.2-IIl.6], and spend enough timeexplaining the proof of Thm 5.2 given in IIl.6. Theparticipants are expected to have read BC91.III.O-IMI.1] before this talk.
Speaker: Prof. Chia-Fu Yu (Institute of Mathematics, Academia Sinica of Taiwan)
Time: 10:30-11:30am November 1, 2023 (Wednesday)
Place: MCM110
Title: On the supersingular locus of Shimura varieties for quaternionic unitary groups
Abstract: We study a Shimura variety attached to a unitary similitude group of a skew-Hermitian form over a totally indefinite quaternion algebra over a totally real number field. We give a necessary and sufficient condition for the existence of skew-Hermitian self-dual lattices, and show that the superspecial locus in the fiber at p of the associated Shimura variety is non-empty. We also give an explicit formula for the number of irreducible components of the supersingular locus when p is odd and unramified in the quaternion algebra. This talk is the joint work with Yasuhiro Terakado and Jiangwei Xue.
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