Curves on compact Shimura surfaces
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Zhehao Li
Time
Monday, October 13, 2025 10:00 AM - 11:00 AM
Venue
Shuangqing-B627
Abstract
We investigate and compare the behaviors of complex curves on two types of compact Shimura surfaces: compact variants of Picard and Hilbert modular surfaces. We will see how complex curves of a fixed genus vanish when the defining discriminant of the Shimura surface grows, and how the special subvarieties and hyperbolic geometry play important roles in the proof. The results can be viewed as special cases of characteristic 0 function field analogs of uniform boundedness on the endomorphism types of abelian varieties.