Academic Report of School of Mathematical Sciences [2026] No. 098

(Series Report for High-Level University Construction No. 1357)

Title：Thurston's sphere packings on 3-dimensional manifolds

Speaker：Professor Xu Xu (Wuhan University)

Time：10:00-11:00, Oct. 21, 2026

Location：Room 1420, Huiwen Building, Yuehai Campus, Shenzhen University

Abstract: Thurston’s sphere packings on 3-dimensional manifolds are 3-dimensional analogues of Thurston’s circle packings on surfaces, and generalizations of the tangential sphere packings introduced by Cooper-Rivin. They could be taken as the discretization of conformal transformations in Riemannian geometry. In this talk, we will discuss the local and infinitesimal rigidity of Thurston’s sphere packings on 3-manifolds. In the special case of tangential sphere packings, we will discuss the global rigidity. This talk is based on joint works with Xiaokai He and Chao Zheng.

Speaker Profile：Xu Xu is a professor and doctoral advisor at Wuhan University, as well as Vice President of the Hubei Mathematical Society. He received his bachelor’s degree from Huazhong University of Science and Technology in 2006 and his Ph.D. from the Institute of Mathematics at the Chinese Academy of Sciences in 2011, where he studied under Researcher Zhang Xiao. He is a Young Top Talent under Hubei Province’s Special Support Program for High-Level Talents. His research focuses on discrete geometry and differential geometry. His representative research achievements include proving the global rigidity of the stacked-sphere metric on three-dimensional manifolds, the rigidity of the inverse distance-stacked-sphere metric on surfaces, and the rigidity of discrete conformal structures of general form on surfaces. He has provided a complete classification of discrete conformal structures on surfaces and has made a series of advances in problems involving prescribed composite curvature and composite curvature flows. He has published more than 40 papers in renowned mathematical journals such as J. Differential Geom., Amer. J. Math., Peking Math. J., Adv. Math., Trans. Amer. Math. Soc., J. Funct. Anal., and Sci. China Math.

Faculty and students are welcome to attend!

Invited by: Zhou Ze

School of Mathematical Sciences

October 19, 2026