Report Title：Combinatorial Yamabe Complexity and the Geometrization of 3-Manifolds
Reporter：Huabin Ge
Affiliation: Renmin University of China
Report Time: September 24, 2026, 10:30–11:30
Report Location: Room 209, Zhengxin Building
Abstract:
Building on three-dimensional sphere packings and the associated framework of variational methods and geometric analysis, this talk introduces combinatorial Yamabe complexity and establishes its comparability with Matveev complexity up to multiplicative constants. After stabilization over finite covers, it is also comparable to the Gromov norm. The stabilized invariant thus detects the hyperbolic pieces in the JSJ decomposition of a 3-manifold and vanishes precisely on graph manifolds.
The unstabilized combinatorial Yamabe complexity, meanwhile, retains finer information, such as the monodromy of mapping tori. Sol manifolds illustrate the difference in the geometric and topological information captured before and after stabilization. These results are based on joint work with Longsong Jia.
Bio:
Huabin Ge received his Ph.D. and completed his postdoctoral research at Peking University. He is currently a Professor and Ph.D. supervisor in the School of Mathematics at Renmin University of China. In 2025, he received funding from the Young Scientists Fund (Category A) of the National Natural Science Foundation of China.
His research focuses on the geometry and topology of 3-manifolds. His collaborative work has generalized Cauchy’s rigidity theorem and Thurston’s circle packing theory, partially resolved Thurston’s geometric triangulation conjecture, and fully resolved related regularity conjectures posed by Cheeger–Tian and Fanghua Lin.
In recent years, his research has developed along two interconnected directions. The first centers on combinatorial Ricci flow and its role in three-dimensional hyperbolization, geometric and topological structures, and Thurston’s geometric triangulations. The second investigates infinite combinatorial structures in topology and their geometric realizations through the study of infinite circle packings and infinite hyperbolic polyhedra, further exploring connections with random walks, boundary theory, and random three-dimensional geometry.
