## Seminar on Conformal Field Theory

**Date:** October 19, 2018

**Place:** Department Mathematik, Cauerstr. 11, 91058 Erlangen

**Speakers:**

- Vassily Gorbounov (University of Aberdeen)
- Jacinta Torres (KIT Karlsruhe)
- Simon Wood (University of Cardiff)

Organisation:

Peter Fiebig, Nils Scheithauer, Katrin Wendland

**Program**

- 14:00 - 15:00: Generalizing LS galleries in affine buildings (Jacinta Torres)
- 15:15 - 16:15: Kac-Moody and Beta-Gamma vertex algebras via factorization algebras approach (Vassily Gorbounov)
- 16:15 - 17:00 :
*Coffee break* - 17:00 - 18:00 : Logarithmic conformal field theory and the Verlinde formula (Simon Wood)

**Abstracts:**

**Kac - Moody and Beta-Gamma vertex algebras via factorization algebras approach**(Vassily Gorbounov)- In the talk using Kac-Moody and Beta-Gamma vertex algebras as an example

we explain the approach to field theories due to K. Costello via factorisation algebras.

- In the talk using Kac-Moody and Beta-Gamma vertex algebras as an example

**Generalizing LS galleries in affine buildings**(Jacinta Torres)- In 2005, Gaussent-Littelmann have interpreted LS galleries in terms of the geometry of affine grassmannians. I will present a generalization of this notion for any Littelmann model of galleries by keeping careful track of the ”load bearing walls” of these galleries. Finally I will present an interpretation of these load-bearing walls in terms of retractions. This is joint work in progress with Petra Schwer.

**Logarithmic Conformal Field Theory and the Verlinde Formula**(Simon Wood)- Arguably one of the greatest achievements of conformal field theory - or rather its algebraic axiomatisation, vertex operator algebras (VOAs) - is Huang's proof of the Verlinde formula for suitably nice VOAs. Nice here essentially meaning that all modules are semisimple and that there are only finitely many isomorphism classes of simples. The Verlinde formula computes fusion products of modules and its inputs are the modular transformations of module characters. In this talk I will discuss some of the obstacles to generalising the Verlinde formula to logarithmic VOAs, that is, VOAs admitting reducible indecomposable modules, and recent progress towards finding such a generalisation.

**Location:**

The seminar will take place in room 04.363. Click here for how to find us.

**Accommodation:**

We reserved a contingent of hotel rooms. If you want to stay overnight please contact Mrs. Helle (helle@math.fau.de)

Dinner:

After the seminar there will be a joint dinner. Please send an email to Mrs. Helle (helle@math.fau.de) if you wish to attend the dinner.

**Further questions:**

If you have any questions please contact the organisers or Mrs. Helle (helle@math.fau.de).