# Thematic School on Quantum Topology and Geometry

- Gaetan Borot (Bonn): "Topological recursion and geometry" Course Notes by Gaetan BorotÂ
- Rinat Kashaev (GenÃ¨ve): "Lectures on TeichmÃ¼ller TQFT" Â Handwritten notes by Rinat Kashaev-part_1 and Part_2
- Thang Q. Le (Atlanta): " The skein algebra of surfaces"
- Julien MarchÃ© (Paris): "Quantum representations of surface groups"

Furthermore during the School one 1 hour "Colloquium" talk will be provided by Dylan Thurston (Bloomington) at IMT.

The deadline for inscriptions is March the 15th 2017.

Go to the **INSCRIPTION FORM**

Organizers: Francesco Costantino and Thomas Fiedler

**Preliminary Schedule**

Â | Tue May 9th 2017 |
Wed May 10th 2017 |
Thu May 11th 2017 |
Fri May 12nd 2017 |
Sat May 13th 2017 |

From 9h30 AM to 10h30 |
Â | Borot | Le | MarchÃ© | Kashaev |

Coffee break 10:30 AM | Coffee |
Coffee |
Coffee |
Coffee |
Coffee |

From 11 AM to 12 AM |
MarchÃ© | Le | Borot | Kashaev | Le |

Lunch 13h00-14h00 AM |
Â | Â | Â | Â | Â |

From 2:00 PM to 3:00 PM |
Borot | MarchÃ© | Kashaev | Thurston | Â |

From 3 to 3h30 PM |
Coffee |
Coffee |
Coffee |
Coffee |
Â |

Until 04:30 PM |
Kashaev | Borot | MarchÃ© | Le | Â |

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**Abstracts of the courses**

*Lectures on TeichmÃ¼ller TQFT (by Rinat Kashaev)*

TeichmÃ¼ller TQFT is a combinatorial model of a three-dimensional TQFT of infinite type where the underlying vector spaces associated with surfaces are infinite dimensional. It is expected to be part of exact quantum Chern-Simons theory with non-compact gauge groups PSL(2,R) and PSL(2,C). There exist two versions of the TeichmÃ¼ller TQFT called Â« old Â» and Â« new Â» formulations which are not equivalent in general but coincide when restricted to integer homology spheres.

*Quantum representations of surface groups (by Julien MarchÃ©)*

In this mini-course we will construct a family of finite dimensional and (pseudo-)unitary representations of surface groups with the following (strange) properties.

They are invariant (up to conjugation) by automorphisms, simple curves have finite order, they are asymptotically faithful.

We will study various (other) aspects of these representations. [following work of Koberda-Santharoubane and M-Santharoubane]

*The skein algebra of surfaces (by Thang Le)*

We present the theory of skein algebra of surfaces. In particular, we will discuss relations between skein algebras and character varieties and quantum Teichmuller spaces, and the structure and representations of skein algebras at a root of 1.

*Topological Recursion and Geometry (by Gaetan Borot)*

Here is a preliminary schedule for the mini-course :

- Topological recursion : introduction (algebraic aspects)
- Hyperbolic geometry : Weil-Petersson volumes of the moduli space of complex curve, after Mirzakhani.
- Cohomological field theories and topological recursion
- Rational conformal field theories and topological recursion

**Participants **

Nezhla | Aghaei |

Vera | Anderson |

Cristina Ana-Maria | Anghel |

Dror | Bar Natan |

Serban | Belinski |

Giulio | Belletti |

RaphaÃ«l | Belliard |

LÃ©o | BÃ©nard |

Gaetan | Borot |

Giulio | Calimici |

Carlo | Collari |

Marco | De Renzi |

Daniel | Douglas |

Travis | Ens |

Matthieu | Faitg |

Thomas | Fiedler |

Nathan | Geer |

Barbara | Giunti |

Pablo | Gonzalez Pagotto |

Kazuo | Habiro |

Jean-Marc | Hok |

Rinat | Kashaev |

Thang | Le |

Cyril | Lecuire |

Christine | Lescop |

david | leturcq |

Daniel | Lopez |

Alessandro | MalusÃ |

Julien | MarchÃ© |

Jules | Martel |

Gregor | Masbaum |

Gwenael | Massuyeau |

Delphine | Moussard |

Dmitry | Noshchenko |

Jinsung | Park |

Michal | Pawelkiewicz |

Jean | Raimbault |

abdoul karim | Sane |

Ramanujan | Santharoubane |

Adam | Sikora |

Kursat | Sozer |

Gilberto | Spano |

Dylan | Thurston |

Vladimir | Turaev |

Huan | Vo |

Tian | Yang |

*(Photo by Patrick Dumas)*

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