2014:
| Date | Speaker | Topic | Notes |
|---|---|---|---|
| 6/2 | Arnaud | The symplectic representation of the mapping class group I | (Farb-Margalit, 6.1 & 6.2) intro to Sp(2g,R) and H_1(S_g,Z); the Euclidean algorithm for curves. |
| 13/2 | Damien D. | The symplectic representation of the mapping class group II | (6.3 & 6.4) the representation, surjectivity onto Sp(2g,Z), congruence subgroups and finite index torsion-free subgroups (proof for Sp(2g,Z); proof for MCG is section 7/talk 4, below). |
| 20/2 | Basile | The Torelli subgroup | Examples of elements (6.5.2); Birman exact sequence; description of an (infinite) generating set & statement of finite generation (6.5.5); action on simple closed curves (6.5.4). |
| 27/2 | Damien T. | Torsion in the mapping class group | Realising finite subgroups of Mod(S_g) as groups of isometries of a hyperbolic surface; Hurwitz' 84(g-1) theorem; finite subgroups admit a faithful symplectic representation. |
| 6/3 | -x- | -x- | -x- |
| 13/3 | Camille | Dehn-Nielsen-Baer Theorem | The theorem says the (extended) mapping class group is isomorphic to the group of outer automorphisms of the fundamental group. |
| Lundi 31/3, 16h30 | Andrew | Introduction to the Nielsen-Thurston Classification | Classifying mapping classes of the torus; periodic, reducible and pseudo-Anosov elements. |
| 27/3 | -x- | -x- | -x- |
| 3/4 (9:30 a.m., la salle viséo - 632) | Christian | Quadratic Differentials | Relating quadratic differentials to measured foliations (11.3); Teichmuller geodesics (11.8 - in particular 11.8.2). |
| 10/4 | -x- | -x- | -x- |
| 17/4 | Damien D. | Moduli space I | Proper discontinuity of the action of Mod(S_g) on Teich(S_g), the length spectrum and Wolpert's Lemma. |
| Lundi 28/4, 14h | Arnaud | Moduli space II | Mumford's compactness criterion. |
| Mardi 29/4, 14h | Basile | Proof of Nielsen-Thurston classification | Collar lemma; proofs that parabolic implies reducible and hyperbolic implies pseudo-Anosov. |
| 1/5 | -x- | -x- | -x- |
| 8/5 | -x- | -x- | -x- |
| 15/5 | -x- | -x- | -x- |
| 22/5 | Arnaud | Relations to other fields I | The link between finite MCG orbits and isomonodromic deformations (and related stuff, like PVI solutions). |
| 5/6 **Room change: 004** | Andrew | Relations to other fields II | Relationships between mapping class groups and arithmetic groups. |
| 19/6 | Camille | Relations to other fields III | Relationships between mapping class groups and outer automorphisms of free groups. |
2013:
| Date | Speaker | Topic | Notes |
|---|---|---|---|
| 17/10 | Andrew | A brief recap on the topology of surfaces | The classification of surfaces; loops, arcs, twists; pants decompositions; diffeomorphisms. |
| 24/10 | Arnaud | Examples of mapping classes and of mapping class groups | Including: disc, sphere, pair of pants, annulus, torus... |
| 31/10 | -x- | -x- | -x- |
| 7/11 | Camille | Curve Complex | Definition, examples, connectedness and other important properties. |
| 14/11 | Basile | Dehn twists I | Definitions and properties, change of coordinates, some relations between Dehn twists. |
| 21/11 | Damien D. | Dehn twists II | Dehn-Likorish Theorem |
| 28/11 | Christian | Introduction to Teichmuller space I | Hyperbolic structures, definition of Teichmuller space, Teich(Pants), Fenchel-Nielsen coordinates. |
| 5/12 | Damien T. | Introduction to Teichmuller space II | Quasiconformal maps and the Teichmuller metric |
| 12/12 | Andrew | The Alexander method and applications | Statement of Alexander method. The MCG has trivial centre, solvable word problem, and trivial abelianisation. |
| 19/12 | -x- | -x- | No workshop - we resume in February. |