This is a research seminar on topics related to number theory and its applications which broadly can include related areas of interests such as analytic and algebraic number theory, algebra, combinatorics, algebraic and arithmetic geometry, cryptography, representation theory etc. The speakers are also encouraged to make their talk more accessible for graduate level students.

For more information, please refer to:http://www.bimsa.cn/newsinfo/647938.html.

Title

Heights of Special Points on Quaternionic Shimura Varieties

Organizers

Hansheng Diao, Yueke Hu,

Heng Du，Bin Xu,

Cezar Lupu, Yihang Zhu

Speaker

Dr. Roy Zhao (YMSC, Tsinghua University)

Time

Mon., 10:00 - 11:00 am, Sept. 23, 2024

Venue

C654, Shuangqing Complex Building A

Abstract

In this talk, we will present an explicit formula for the height of a special point on a quaternionic Shimura variety in terms of Faltings heights of CM abelian varieties. This improves upon Yuan and Zhang’s work on the height of points on quaternionic Shimura curves. We will also discuss applications of this formula to proving the Large Galois Orbits Conjecture, an ingredient in the Pila—Zannier strategy for proving the Andre—Oort conjecture for Shimura varieties. We then contrast this formula with the one given by Pila, Shankar, and Tsimerman.

About the speaker

Dr. Roy Zhao

YMSC, Tsinghua University

Research Areas

Arakelov Geometry, Arithmetic Geometry, Shimura Varieties, Unlikely Intersections

Education

2017.08 - 2023.08 Ph.D. in Mathematics, University of California -- Berkeley

2013.09 - 2017.06 B.S. in Mathematics Princeton University

Publications

1. Algebraic Independence of Special Points on Shimura Varieties (with Yu Fu), Submitted.

2. Heights of Special Poitns on Quaternionic Shimura Varieties, Submitted.

3. Algebraic Varieties and Automorphic Functions (with Sebastian Eterovic), Submitted.

Personal Homepage：

https://ymsc.tsinghua.edu.cn/en/info/1035/3017.htm