Academic reports of Haitian scholars—Professor Andrei Vesnin
Report: Prof. Andrei Vesnin (Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences)
Title: Introduction to Hyperbolic 3-Manifolds
Location: A1101#room, Innovation Park Building
Abstract: 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.
The brief introduction to the reporter: 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 research interests include low-dimensional topology, knot theort, hyperbolic geometry, combinatorial group theory, graph theory and applications.
In 2008, Prof. Vesnin was elected to corresponding member of the Russian Academy of Sciences.
Report 1
Title: Hyperbolic plane: models, geodesics, isometries
Time: December 21, 2016 PM 3:30-5:10
Report 2
Title: Hyperbolic trigonometry
Time: December 22, 2016 PM 3:30-5:10
Report 3
Title: Hyperbolic space. Hyperbolic polyhedral
Time: December 23, 2016 PM 3:30-5:10
Report 4
Title: Lobachevsky function. Volumes of polyhedra
Time: December 26, 2016 PM 3:30-5:10
Report 5
Title: Kleinian groups, Fundamental polyhedral
Time: December 27, 2016 PM 3:30-5:10
Report 6
Title: Gluing of manifolds，Mostow rigidity theorem
Time: December 29, 2016 PM 3:30-5:10
Report 7
Title: Volumes of manifolds, Thuston-Jorgensen theorem
Time: December 30, 2016 PM 3:30-5:10
Report 8
Title: Fibonacci manifolds and Loebell manifolds
Time: January 2, 2017 PM 3:30-5:10
Report 9
Title: Knot and link complements
Time: January 3, 2017 PM 3:30-5:10
Report 10
Title: Tetrahedral hyperbolic manifolds
Time: January 4, 2017 PM 3:30-5:10
References:
[1] J.G. Ratcliffe, Foundations of hyperbolic manifolds.
[2] R. Benedetti, C. Petronio, Lectures on hyperbolic geometry.
窗体顶端
School of Mathematical Sciences
Dalian University of Technology
窗体底端
December 12, 2016
