Title：Combinatorial curvature flows with applications to 3-dimensional geometry and topology
Speaker：葛化彬 （北京交通大学）
Time: 7月17日,08:30-11:30;
7月18日,08:30-11:30;
7月19日,08:30-11:30.
Room：东区管理科研楼 数学科学学院1418室
Abstract：This is an introductory lecture on combinatorial Ricci/Calabi/Yamabe flows and the characterizations on convex (ideal) polyhedrons in hyperbolic 3-space. We will begin with Thurston’s circle pattern theorem and end with a combinatorial Ricci flow proof of Rivin’s characterizations about ideal convex hyperbolic polyhedrons (Ann. of Math. 1996). The course will cover the following topics:
1) The definition of combinatorial Ricci/Calabi/Yamabe flows.
2) The rigidity of (finite or infinite) circle patterns.
3) Basic hyperbolic geometry.
4) The rigidity of hyperbolic (ideal) convex polyhedrons.
5) The existence of hyperbolic (ideal) convex polyhedrons.