关于举行北京交通大学葛化彬副教授学术报告的通知

报告题目：Characterizing ideal polyhedra in hyperbolic 3-space by combinatorial and angle structure
报 告 人：葛化彬 副教授 (北京交通大学)
报告时间：2017年12月08日 （星期五） 上午09:00-10:00
邀 请 人：杜晓明 博士
报告地点：四号楼4318室

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                                                                      数学学院
                                                                  2017年12月05日

报告摘要：Around 1980, Thurston showed that “almost every” 3-manifold admits a complete hyperbolic metric. To get such a metric, he proposed to ideally triangulate the manifold and realize each tetrahedron as a hyperbolic ideal tetrahedron. He also gave a system of gluing equations in the shape parameter of these ideal tetrahedrons, whose solution corresponds to the complete hyperbolic metric.
    In the 1990s, Casson discovered a powerful technique for solving Thurston's gluing equations. The main idea is to study the combinatorial structure of the triangulation and the dihedral angle structure of each tetrahedron. Following Casson's program, Rivin completely describes all convex ideal polyhedra by combinatorial and angle structures.
    In this talk, we shall use combinatorial Ricci flow methods, initiated by Bennett Chow and Luo Feng, to approach Casson-Rivin's program. We shall extend Koebe-Andreev-Thurston's Circle Pattern Theorem, Rivin's theorem on ideal hyperbolic polyhedra and Chow-Luo's theory on combinatorial Ricci flows. Our results suggest an algorithm exponentially fast to find (ideal) circle patterns and ideal hyperbolic tetrahedrons with the given combinatorial type and dihedral angles. This is joint work with Hua Bobo and Zhou Ze.
报告人简介：葛化彬，北京交通大学副教授。主要的研究方向是几何分析和低微几何拓扑。部分研究工作已经发表在 GAFA, Adv. Math, IMRN, Math. Ann., Trans. AMS, CVPDE, JFA 等知名期刊上。