Tan Kah Kee Young Scientist Award

Mathematics & physics

Yichao Tian

Yichao Tian was graduated from Tsinghua University with a bachelor's degree in 2004. Then he received his Ph.D. from University Paris 13 in France in June 2008, under the supervision of Professor Ahmed Abbes. After that, he worked as a postdoc for 3 years at Princeton University in the United States. Since July 2011, he has been a faculty member in the Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He visited the University of Bonn in Germany from 2015 to 2018 and the University of Strasbourg in France from 2018 to 2021.

The research area of Yichao Tian is arithmetic algebraic geometry and number theory. In his Ph.D. thesis, he gave a sufficient condition for the existence of canonical subgroups of p-divisible groups. More recently, he has been studying the geometric properties of Shimura varieties in characteristic p and applied them to important problems in number theory, such as the Tate conjecture over finite fields, the classicality of p-adic modular forms, and the Beilinson-Bloch-Kato conjecture on the relationship between L-functions and Selmer groups.

Yichao Tian was sponsored by the National Science Fund for Oversea Young Scholars in 2011, by the National Science Fund for Distinguished Young Scholars in 2022. He received the Young Scientist Award of Chinese Academy of Sciences in 2022.

**p-adic geometry of Shimura varieties and arithmetic application**

Shimura varieties are important geometric objects in modern arithmetic algebraic geometry. They include as special examples the classical moduli spaces such as modular curves, Hilbert modular varieties, Siegel moduli spaces. Shimura varieties play an important role in Langlands program. By studying their geometric properties, one can establish many deep relations between Galois representations and automorphic forms predicted by the Langlands program.

In a series of work, Yichao Tian and his collaborator described the global geometry of the Goren--Oort stratum on Hilbert modular varieties over a finite field. Moreover, they used those geometric results to give cohomological proof on the classicality of overconvergent Hilbert modular forms, and got new results on the Tate conjecture for Hilbert modular varieties in high codimensions. More recently, Yichao Tian and another group of collaborators used the geometry of unitary Shimura varieties in characteristic p to prove new instances of Beilinson--Bloch--Kato conjecture for motives of Rankin--Selberg type in the rank 0 and 1 case. Such a result is one of rare results in this field that hold for a family of motives.