Thematic School on Quantum Topology and Geometry

The school will begin on may the 9th and end on may the 13th 2017 at IMT, Toulouse.

Four mini courses will be provided by:

• Gaetan Borot (Bonn): "Topological recursion and geometry" Course Notes by Gaetan Borot 
• Rinat Kashaev (Genève): "Lectures on Teichmüller TQFT"   Handwritten notes by Rinat Kashaev-part_1 and Part_2n see also the notes by Nezhla Aghaee  lecture_notes-rinatkashaev-notes_by_nezhlaaghaee.pdf
• Thang Q. Le (Atlanta): " The skein algebra of surfaces"
• Julien Marché (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

Abstracts of the courses

Lectures on Teichmüller TQFT (by Rinat Kashaev)
Teichmüller 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 Teichmüller TQFT called « old » and « new » formulations which are not equivalent in general but coincide when restricted to integer homology spheres.

Quantum representations of surface groups (by Julien Marché)

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 :

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

Participants

(Photo by Patrick Dumas)