【the Alexader Grothendieck Institute in Montpellier, France】— Professor Vladimir Vershinin

2016-10-26

Reports of Braid Groups and related topics

Reporter: Prof. Vladimir Vershinin (the Alexader Grothendieck Institute in Montpellie, France)

Series Report titles: Braid groups and related topics

Contact: LEI Fengchun (tel: 84706472)

Series report abstract:

1. Configuration spaces.

2. Definitions of braid groups.

3. Presentations of braid groups, pure braid groups, Markov normal form.

4. Braid group as a subgroup of automorphism group of a free group and as amapping class group of a punctured disc.

5. Algebraic proprieties of braid groups, theorems of Garside.

6. Presentation of Birman, Ko and Lee.

7. Representation of braids, theorem of Bigelow and Krammer.

8. Theorem of Dehornoy about ordering of braid groups.

9. Theorems of Alexander and Markov.

10. Generalisations of braids : braids of surfaces, singular braids, virtual, groups

11. Artin-Tits, etc.

12. Cohomology of braids.

13. Braid groups and Lie algebras.

14. Brunnian braids.

Brief introduction to the reporter: Professor Vladimir Vershinin is a professor of mathematics at the Alexader Grothendieck Institute in Montpellier, France, and a researcher at the Sobolev Institute of Mathematics, Novosibirsk, Russia. He had hold one year visiting position in Autonoma University of Barcelona, Spain, half year positions in the IHES, Paris, France, and the Poncelet Laboratory, Moscow, Russia. His interests in Mathematics include mainly Algebraic Topology, and braid groups and their generalizations. In Aplied Mathematics he worked in the domains of Approximation Theory and Mathematical Methods in Chemistry. In is recent joint work with Wu Jie and Li Jingyan the authors studied connections between Brunnian braids and Lie algbras.

Series Report Scheduling:

Report 1.

Report time: May 17, 2016 PM 3:00-5:00