9:30 - 10:30am Chenyang Xu, Boundedness of automorphism groups.

Abstract: (joint work with Christopher Hacon and James McKernan) For a smooth general type variety X, we proved the order of the automorphism group jAut(X)j is always bounded linearly by vol(KX), where the coefficient of the linear function only depends on the dimension of X. If time permits, we will discuss a stronger theorem in the direction of boundedness of volumes, as well as its application to the moduli problem of stable varieties (in higher dimensions).

10:45 - 11:45am Huayi Chen, Heights of arithmetic varieties.

Abstract: We discuss several definitions of heights of arithmetic varieties and their relations.

Lunch

1:30 - 2:30pm Xinwen Zhu, Local models and Schubert varieties

Abstract: Local models serve as tools to study the local geometry of Shimura varieties. They are schemes ´etale locally isomorphic to local Shimura varieties, but are defined in terms linear algebra and are therefore much simpler to study. The special fibers of local models are closely related to Schubert varieties in the affine flag varieties. I will discuss this connection and verify a conjecture of Pappas and Rapoport.

2:45 - 3:45pm Yifeng Liu, L-values via theta lifting.

Abstract: One of the most important objects in number theory and automorphic form is the L-function and especially its value or derivative at the center. I will talk about one way to detect them which is the theta lifting and its arithmetic analogue. To be simple, I will only focus on the unitary group of two variables over rational numbers. If time permits, I will talk about some applicatations or generalization.

Tea

4:30 - 5:30pm Yuancao Zhang, Analytic vectors in unitary principle series

representations of GL(2;Qp)