Overview poster for the Master Classes in 2007

**Abstract:**

Let *S* be a compact oriented surface of genus *g* with *b* boundary
components. The mapping class group $\Gamma=\Gamma_{g,b}$ of *S* is
the group of orientation-preserving homeomorphisms of *S* up to isotopy.

The study of the group $\Gamma$ started with the very beginning of
the subject of low-dimensional topology.

The algebraic properties of this group were obtained by studying its
actions on various spaces, and these actions revealed beautiful
geometric properties of that group. More recently, this group appeared
as a central object in various quantization theories of moduli spaces.

In this master class, I shall talk about the following topics :

- Generators and relations for $\Gamma$, in particular the Dehn-Likorish generators and the order-two generators.
- The action of $\Gamma$ on the Teichmüller space of the
surface
*S*, in particular the dynamics of this action with respect to the Teichmüller and the Weil-Petersson metrics. - The action of $\Gamma$ on Thurston's boundary of Teichmüller space: dynamics, limit sets and domains of discontinuity.
- The action of $\Gamma$ on the Harvey curve complex, the arc complex, the complex of domains, on the complex of boundary graphs and on other simplicial complexes. In each case, I will analyze the mapping class group as compared to the simplicial automorphism group of the complex, and the geomery and dynamics of the actions of $\Gamma$ on the simplicial complex equipped with its simplicial metric.

On each topic, I will try to give an overview on part of the work done, and I will explain in more detail old and recent joint work with John McCarthy.

Professor Athanase Papadopoulos will be visiting CTQM from 2-20 April 2007.

The schedule for the Master Class is as follows:

Tuesdays and Wednesdays in Weeks 14-16,

Koll. G, Bldg. 1532, 2nd floor

Tuesday 3 April to Wednesday 18 April:

11:00-11:45 Lecture

11:45-12:15 Coffee Break

12:15-13:00 Lecture

NB: A Master Class dinner will take place on 17 April 2007.

All recordings are in *MOV*-format and playable by either
QuickTime or VLC.

- Lecture 1 Small size (192M) Larger size (802M)
- Lecture 2 Small size (211M) Larger size (764M)
- Lecture 3 Small size (166M) Larger size (689M)
- Lecture 4 Small size (207M) Larger size (745M)
- Lecture 5 Small size (200M) Larger size (719M)
- Lecture 6 Small size (180M) Larger size (644M)
- Lecture 7 Small size (198M) Larger size (718M)
- Lecture 8 Small size (188M) Larger size (680M)
- Lecture 9 Small size (172M) Larger size (714M)
- Lecture 10 Small size (183M) Larger size (663M)
- Lecture 11 Small size (189M) Larger size (682M)
- Lecture 12 Small size (224M) Larger size (806M)

Supplementary funding for this master class is provided by "Forskerskole i Matematik og anvendelser" based at the Department of Mathematics, University of Copenhagen.

Revised 20.03.2008

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