海天学术大师Andrei Vesnin教授系列学术专题讲座

报 告 人： Andrei Vesnin教授(Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences; 俄罗斯科学院通讯院士)

讲座题目：Introduction to Hyperbolic 3-Manifolds

讲座摘要：The aim of the course is to give a short introduction to building of hyperbolic 3-manifolds and calculating their invariants such as a volume. We will recall some basic properties of hyperbolic geometry as a base for further calculations. We will prove existence for some classes of hyperbolic polyhedra and will find their volume formulae. Then we will use the polyhedra to construct series of compact and non-compact hyperbolic 3-manifolds. Finally, we will discuss properties of the volume set which will be illustrated by manifolds constructed.

报告地点：创新园大厦A1101

报告人简介：Professor Andrei Vesnin is head of the Laboratory of Applied Analysis, Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences and a professor of Geometry and Topology, Novosibirsk State University. He received a Candidate of Sciences in physics and mathematics is 1991 from Sobolev Institute of Mathematics for the thesis “Discrete groups of reflections and three-dimensional manifolds”, and a Doctor of Sciences in physics in mathematics in 2005 for the thesis “Volumes and isometries of three-dimensional hyperbolic manifolds and orbifolds”.

   Professor Vesnin's reseach interests include low-dimensional topology, knot theory, hyperbolic geometry, combinatorial group theory, graph theory and applications.

In 2008， Professor Vesnin was elected to corresponding member of the Russian Academy of Sciences.

讲座1

报告题目：Hyperbolic plane: models, geodesics, isometries

报告时间：2016年12月21日（Wed）下午3:30-5:10

讲座2

报告题目：Hyperbolic trigonometry

报告时间：2016年12月22日（Thu）下午3:30-5:10

讲座3

报告题目：Hyperbolic space. Hyperbolic polyhedral

报告时间：2016年12月23日（Fri）下午3:30-5:10

讲座4

报告题目：Lobachevsky function. Volumes of polyhedra

报告时间：2016年12月26日（Mon）下午3:30-5:10

讲座5

报告题目：Kleinian groups, Fundamental polyhedral.

报告时间：2016年12月27日（Tue）下午3:30-5:10

讲座6

报告题目：Gluing of manifolds，Mostow rigidity theorem

报告时间：2016年12月29日（Thu）下午3:30-5:10

讲座7

报告题目：Volumes of manifolds, Thuston-Jorgensen theorem

报告时间：2016年12月30日（Fri）下午3:30-5:10

讲座8

报告题目：Fibonacci manifolds and Loebell manifolds

报告时间：2017年1月2日（Mon）下午3:30-5:10

讲座9

报告题目：Knot and link complements

报告时间：2017年1月3日（Tue）下午3:30-5:10

讲座10

报告题目：Tetrahedral hyperbolic manifolds

报告时间：2017年1月4日（Mon）下午3:30-5:10

推荐参考书目：

[1] J.G. Ratcliffe, Foundations of hyperbolic manifolds.

[2] R. Benedetti, C. Petronio, Lectures on hyperbolic geometry.

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2016年12月12日