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Academic reports of Haitian scholars—Professor Andrei Vesnin



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 manifoldsMostow 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




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

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



School of Mathematical Sciences

Dalian University of Technology


December 12, 2016