School of Mathematical Sciences Academic Report [2025] 047
(High-Level University Construction Series Report No. 1069)
Lecture Title: Rigidity of holomorphic map between bounded symmetric domains preserving Shilov boundaries
Speaker: Assoc. Prof. Yun Gao (Shanghai Jiao Tong University)
Date & Time: 2:30 - 3:30 PM, June 24, 2025
Venue: Room 1420, Convergence Building
Abstract: The study of rigidity of holomorphic maps originated from the work of Poincaré and later Alexander for maps sending one open piece of the sphere into another. Webster obtained rigidity for holomorphic maps between pieces of spheres of different dimension, proving that any such map between spheres in C^n and C^{n+1} is totally geodesic. There are plenty of results about the holomorphic proper mapping between balls and generalized balls. The rigidity for maps between bounded symmetric domains are more complicated. Mok conjectures that If the rank r of D does not exceed the rank r’of D’and both ranks r,r’>1, then the proper holomorphic maps is totally geodesic. There are some results about this conjecture. In 2007, Kim and Zaitsev proved the rigidity of locally defined CR embeddings between Shilov boundaries of general Cartan type I bounded symmetric domains of higher rank. In this talk, we will introduce a different method coming from algebraic geometry to study this kind of map and prove the rigidity of holomorphic mapping between bounded symmetric domains preserving Shilov boundaries from rank 1 bounded symmetric domains to higher rank.
Biography: Yun Gao, Associate Professor at Shanghai Jiao Tong University, specializes in algebraic geometry and complex geometry. His research has been published in renowned academic journals including J. Math. Pures Appl., Math. Ann., and Int. Math. Res. Not. IMRN. He has led and participated in multiple projects supported by the National Natural Science Foundation of China.
All faculty and students are welcome to attend!
Invited by: Cong Ding
School of Mathematical Sciences
June 19, 2025
