Seminar| Institute of Mathematical Sciences
Time: Monday, September 28th, 2026,16:00-17:00
Location: IMS RS506
Speaker: Sicheng Lu, Suzhou University
Abstract: HCMU metrics are extremal Kähler metrics on compact Riemann surfaces with a finite number of singularities. Research on these metrics was initiated by E. Calabi over forty years ago. This lecture series will focus on HCMU surfaces of fixed genus with prescribed cone angles and their geometric moduli spaces.
Starting from the classical football decomposition, we use mixed-angulations of surfaces, weighted bipartite graphs, and geometric parameters to develop a combinatorial + geometric data set representation of generic HCMU surfaces. Within this framework, we give a unified proof of the angle constrains for existence, and investigate the existence of HCMU surfaces of arbitrary genus with a single conical singularity. Finally, we compute the dimensions of the moduli spaces using geometric deformations and balance equations on graphs. This is a joint work with Bin Xu from USTC.
The series consists of four lectures:
1. Geometric decompositions of HCMU surfaces and other surfaces with conical singularities
2. Representing HCMU surfaces by combinatorial and geometric data
3. From weighted graphs to surfaces: existence and the case of a single conical singularity
4. Geometric deformations, moduli space dimensions, and further developments