Alternatively have a look at the program.

## The Hitchin connection and the Witten-Reshetikhin-Turaev TQFT, I

*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.*

## The Hitchin connection and the Witten-Reshetikhin-Turaev TQFT, I

## Graphical obstructions to the surjectivity of the higher order Johnson homomorphism

The Johnson filtration of the mapping class group gives rise to an associated graded Lie algebra. The higher order Johnson homomorphism embeds this Lie algebra in the larger but better understood Lie algebra of symplectic derivations. It has long been known that this is not surjective, and various families of obstructions to surjectivity have been constructed by several authors. We give a graph homology construction that unifies and expands all of the previously known obstructions (with one exception, the so-called Galois obstruction.)

## Topological recursion and moduli spaces, I

*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.*

## Topological recursion and moduli spaces, I

## Automorphic forms for mapping class groups from conformal field theory.

Rational conformal field theories on elliptic curves yield

easily computable modular forms. This fact generalizes to higher genus.

## The Hitchin connection and the Witten-Reshetikhin-Turaev TQFT, II

## The Hitchin connection and the Witten-Reshetikhin-Turaev TQFT, II

## Review: relations between Chern-Simons theory and topological recursion

Up to now, Chern-Simons theory has been related to topological recursion in two different regimes. Firstly, considering SU(N + 1) theory in Seifert fibered spaces, the large N expansion of the colored (in any fixed representation R) HOMFLY invariant of fiber knots, can be extracted from a topological recursion.

## Topological recursion and moduli spaces, II

© MPI f. Mathematik, Bonn | Impressum & Datenschutz |