## School program

## Andre Henriques, "Conformal nets"

Beginning with a general description of type III von Neumann algebras,
I will proceed to define conformal nets. The latter are a model for conformal
field theories, and I will discuss various examples there of (free fermions;
free bosons; loop groups).

I will then explain the famous result of Kawahigashi, Longo, Mueger according to which conformal nets with finite mu-index have a representations category that is modular.

Depending on the progress of my own understanding, I might introduce a 3-dimensional graphical calculus for computations in conformal nets.

I will then explain the famous result of Kawahigashi, Longo, Mueger according to which conformal nets with finite mu-index have a representations category that is modular.

Depending on the progress of my own understanding, I might introduce a 3-dimensional graphical calculus for computations in conformal nets.

## Bernhard Keller, "Cluster algebras and triangulated categories"

TBA

## Aaron Lauda, "Categorifying quantum groups"

Geometric representation theory has a revealed a deep
connection between geometry and quantum groups suggesting that
quantum groups are shadows of richer algebraic structures called
categorified quantum groups. Crane and Frenkel conjectured that
these structures could be understood combinatorially and applied to
low-dimensional topology. In this lecture series we will categorify
quantum groups using a simple diagrammatic calculus that requires no
previous
knowledge of quantum groups. We will discuss 2-categories and how they
serve as a natural environment for turning algebraic problems into
planar diagrammatics that can be manipulated using topological
intuition.

We will also survey the applications of categorified quantum groups including a new grading on blocks of the symmetric group and Webster's recent work categorifying Reshetikhin-Turaev invariants of tangles.

We will also survey the applications of categorified quantum groups including a new grading on blocks of the symmetric group and Webster's recent work categorifying Reshetikhin-Turaev invariants of tangles.

## Thomas Willwacher, "M. Kontsevich's graph complex and the Grothendieck-Teichmüller Lie algebra"

The graph complex and the Grothendieck-Teichmüller Lie algebra are
probably two of the most mysterious
(dg) Lie algebras appearing in mathematics. We will recall their
definitions and basic properties. Furthermore, we will discuss their
role in Deformation Quantization and see explicit maps relating both
objects.