Abstracts

- Katrina Barron (University of Notre Dame): "On twisted constructions for vertex operator algebras"

We will discuss some of the known twisted constructions for vertex operator algebras and implications for the construction and classification of twisted modules in terms of other twisted and non-twisted modules.

- Christopher Beem (University of Oxford): "Quasi-Lisse VOAs from four dimensions"

I will outline a correspondence between vertex operator algebras and four-dimensional superconformal field theories, and describe some properties of the VOAs that arise in this fashion. In general these are irrational VOAs, but they satisfy a natural finiteness condition generalizing C2-cofiniteness. This leads to interesting modular properties of certain VOA characters and suggests a strong geometric underpinning for this class of algebras.

- Matthew Buican (Queen Mary University of London): "Comments on Galois Groups and QFTs"

I will present some results on the action of Galois groups on field theories in different dimensions. In particular, I will discuss their appearance in classes of RG flows between 4D N=2 superconformal field theories via certain 4D/2D correspondences. Time permitting, I will explain new results on Galois group actions in other classes of theories.

- Miranda Cheng (Universiteit van Amsterdam): "3-manifold invariants and log CFTs"

My talk will be about a certain quantum invariants for three-manifolds. I will discuss the definition, the modular properties of these invariants and the observed relation to log CFTs. The talk will be based on the preprint 1809.10148 and work in progress with Chun, Feigin, Gukov, Ferrari, and Harrison.

- Terry Gannon (University of Alberta): "Fantastic beasts and where to find them"

The boring and well understood CFTs are the rational ones closely related to classical mathematics like simple Lie algebras and finite groups: e.g. the WZW models, lattice models, ... A natural way to move beyond these is to drop rationality and explore other classes of CFTs built from classical math, e.g. the W-algebras. Of course in doing this we will also obtain new classes of rational CFT, but that is an accidental biproduct; the main purpose of this important exercise is to develop and explore friendly "classical" examples beyond the rational setting. But there is another road, less travelled by: there appear to be large classes of not-yet-constructed rational CFTs which have no known relation to classical math. The evidence supporting their existence comes from subfactor methods. These hypothetical RCFTs (the fantastic beasts of the title) share a similar look, which suggests there should be a new way to construct CFTs, beyond GKO cosets and group orbifolds. Of course this construction will also presumably work beyond rationality, and there are surely new classes of nonrational CFTs which can come from these subfactor methods. But before we go there, I'd suggest to develop and explore friendly rational examples beyond the "classical" setting. My talk will be on this road less travelled by.

- Simon Lentner (Universität Hamburg): "Examples of Nonsemisimple Modular Tensor Categories in Conformal Field Theory"

The representation category of a suitably finite vertex algebra is a braided tensor category by works of Huang, Lepowsky, Zhang.

As motivating example I will discuss the new, but entirely not surprising, non-semisimple representation theory of the Heisenberg Vertex algebra, which is equivalent to the (infinite) representation theory of the polynomial ring C[X] with a particularly structure of a quasi-triangular Hopf algebra. The main part of my talk is ongoing work with Y.-Z. Huang about screening operators, which give in a very general setting an action of a Nichols algebra, and, as I would further conjecture, as Kernels new Vertex subalgebras with non-semisimpe representation theory related to these Nichols algebras. The result generalizes an earlier result of mine in the context of lattice vertex algebras and quantum groups.

- Ehud Meir (University of Aberdeen): "Geometric invariant theory and Hopf algebras"

Geometric invariant theory (GIT) has applications in several areas of the theory of Hopf algebras.

It can be used to find a complete set of scalar invariants for semisimple Hopf algebras and for Hopf cocycles, and also to study non-semisimple Hopf algebras in braided monoidal categories.

In this talk I will explain how scalar invariants can be used to prove the finite number of Hopf orders of a given finite dimensional semisimple Hopf algebra, and an ongoing work about the rigidity of Nichols algebras.

- Christoph Schweigert (Universität Hamburg): "Bulk Fields in Conformal Field Theory"

In this talk, we present recent results on fields and on correlators for conformal field theories beyond rational conformal field theories, for chiral data that are described by non-semisimple categories.

- Anne Taormina (Durham University): "Quarter BPS states at the Kummer point and the symmetry surfing programme"

The elliptic genus of K3 surfaces encrypts an intriguing connection between the sporadic group Mathieu 24 and non-linear sigma models on K3, dubbed `Mathieu Moonshine'. By restricting to Kummer K3 surfaces, which may be constructed as Z_2 orbifolds of complex 2-tori with blown up singularities, and in work done in collaboration with Katrin Wendland, it has been possible to devise a framework in which our concept of symmetry surfing can be explored and tested in a concrete way.

This talk focusses on what has been learned so far that supports the symmetry surfing idea when lifting the Kummer construction to the level of conformal field theory, with particular emphasis on quarter BPS states. Some of these states enter the elliptic genus with opposite signs thus cancelling each other when counted by this partial index, yet they carry interesting information that should help understand Mathieu Moonshine.