Workshop: Geometric quantization and topological recursion

Goal: The workshop aims at establishing bridges between the geometric quantization of moduli spaces, and the theory of the topological recursion, continuing earlier discussions initiated by some of the participants. As an application, we have in view the understanding of the all-order asymptotics of quantum knot invariants, like the knot state ensuing from the Witten-Reshetikhin-Turaev construction, or the colored Jones polynomial.

At this occasion, two 5h mini-courses will be held, 9h-11h every day of the week:

Recordings of the mini-courses are available here [5]

The Hitchin connection and the Witten-Reshetikhin-Turaev TQFT
Jørgen Ellegaard Andersen (QGM Aarhus)

We will review the relevant moduli spaces of flat connections which forms the corner stone in the construction of quantum Chern-Simons theory from a gauge theory point of view. We will further review the construction of the Hitchin connection in the bundles over Teichmüller space, which are obtained by applying geometric quantization to these moduli spaces. Following this, we will discuss the asymptotics of the Hitchin connection near certain points on the Thurston boundary of Teichmüller space. This will allow us to define both, the unitary structure preserved by the Hitchin connection, the handlebody boundary state vector and curve operators. We will then discuss their relations to Toeplitz operators and obtain asymptotics results about these TQFT. If time allows, we will also discuss quantum Chern-Simons theory with complex gauge group.

Topological recursion and moduli spaces
Bertrand Eynard (IPHT CEA Saclay & CRM Montréal)

The lecture will start with an introduction to the topological recursion. Then, we shall explain the proof of the theorem relating topological recursion to integrals over moduli spaces of curves. The last part will focus on the notion of quantum curves. Some explicit examples will be treated, in particular the finite reductions of KdV.

Extra talk on Wednesday 26, 4.30pm:

Topological recursion for Chern-Simons theory

Gaetan Borot

We will review what is known on the application of topological recursion to Chern-Simons theory, and informally summarize the relations we expect between geometric quantization of character varieties and topological recursion.

Extra talk on Friday 28, 1.00pm (Seminar room, next to Lecture Hall):

Hitchin system and quantum curves

Motohico Mulase

Two regular MPIM seminars will be related to the topic of the workshop:

Topology seminar, Monday 4.30pm

Graphical obstructions to the surjectivity of the higher order Johnson homomorphism

Jim Conant

Oberseminar, Thursday 3.00pm

Givental quantization procedure and computation of Gromov-Witten invariants by topological recursion

Nicolas Orantin

The remaining time will be devoted to discussions among the participants.

Participants: Raphaël Belliard, Leonid Chekhov, James Conant, Olivia Dumitrescu, Gregor Masbaum, Pavel Mnev, Motohico Mulase, Werner Nahm, Nicolas Orantin, François Petit, Nuño Romao, Emanuel Scheidegger, Shehryar Sikander, Tom Sutherland, Szilard Szabo, Roland van der Veen.

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[6]Annonce.pdf [7]	142.08 KB
[8]Schedule.pdf [9]	226.84 KB