### Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

#### Posted by Urs Schreiber

In May there is the following workshop in Cardiff:

*Workshop on Higher Gauge Theory, TQFT and Categorification*Monday 9th - Tuesday 10th May 2011

School of Mathematics, Cardiff University

organized by WIMCS, more precisely by the *Mathematical Physics Cluster of the Wales Institute of Mathematical and Computational Sciences*. Timothy Porter is doing the organisation of the programme whilst the hard work is being done by Mathew Pugh and David Evans down in Cardiff.

Below are some of the speakers, talk titles and abstracts. The list is incomplete. If you are a speaker and would like more information about your talk be visible here, please send me an email.

Aristide Baratin (Orsay, Paris)

**State sum invariant from a 2-category****Abstract:**‘State sum models’ are discrete functional path integrals. Using the combinatorics of the Pachner moves of the triangulation to convert a topological problem into an algebraic one, these models can be used to define manifold invariants and topological quantum field theories. Just as 3d state sum models can be built using categories of group representations, 2-categories of 2-group representations may provide interesting state sum models for 4d quantum topology, if not quantum gravity. I will describe the construction of the first non-trivial example of a such models, based on the representations of the ‘Euclidean 2-group’, built from the rotation group SO(4) and its action on the translation group of Euclidean space. I will show that this model gives a new way to compute Feynman integrals for ordinary quantum field theories on 4d Euclidean spacetime.Benjamin Bahr (Cambridge)

**State-sum models and coarse graining in quantum gravity****Abstract:**In this talk a general framework will be reviewed, in which to formulate physical theories discretized on two-complexes, being closely related to manifold invariants constructed from TQFTs. Examples for such theories are Lattice gauge theories, Ising spin systems, and in particular the Spin Foam approach to quantum gravity. In the rest of the talk, the problem of finding a continuum limit for the discretized theories is discussed, and it is shown how this is related to constructing triangulation-independent state-sum models, and renormalization in statistical field theories.Jeffrey Giansiracusa (Bath)

**Topological field theory and deformation theory****Abstract:**This is a speculative talk about some very early stage research in progress. Costello proved that an open string topological conformal field theory is essentially the same as an $A_\infty$ algebra, and that an open TCFT has a universal closed counterpart that is closely related to the deformation theory of the open part. Recently B. Cooper found a $C_\infty$ analogue of Costello’s theorems. I’ll discuss these theorems and how they points towards the possibility of a generalized Deligne Conjecture that would construct from any (cyclic or modular) operad $P$ the universal algebraic structure acting on the deformation theory of $P$-algebras.Alexander Kahle (Göttingen)

**Higher Abelian Gauge Theory and Differential Cohomology****Abstract:**In this talk I will describe how the subject of differential cohomology gives a useful framework for discussing higher gauge theory, and is in some sense necessitated by Dirac charge quantisation. The talk will be example driven, and I hope to discuss ordinary and higher Maxwell theory, as well as some of the theory of Ramond-Ramond fields and D-Branes, and how (twisted) K-theory enters the picture there. Time permitting, I will mention some recent work with Alessandro Valentino investigating T-Duality in this context.Jeffrey Morton (Lisbon)

**ETQFT by Induced Representations****Abstract:**Extended topological quantum field theory (ETQFT) is the categorification of ordinary TQFT, described in terms of a 2-functor from a cobordism category into 2-vector spaces. I describe how a class of such ETQFT’s can be given, one for any finite group G, via gauge theory. This uses a universal construction a category of groupoids and spans, through the adjunction between restriction and induction of representations. I will describe this construction and sketch the generalization to (compact) Lie groups.Urs Schreiber (Utrecht)

**$\infty$-Connections and their Chern-Simons functionals****Abstract:**I indicate a general theory of higher gauge fields/higher connections and how they naturally come with their higher Chern-Simons functionals / Chern-Weil homomorphisms. Then I demonstrate some applications to supergravity, such as the description of the Green-Schwarz mechanism by twisted differential string structures.(aspects of chapter 4 of differential cohomology in a cohesive topos)

Jamie Vicary (Oxford)

**123 TQFTs****Abstract:**Abstract: I will present some new results on classifying 123 TQFTs, using a 2-categorical approach. The invariants defined by a TQFT are described using a new graphical calculus, which makes them easier to define and to work with. Some new and interesting physical phenomena are brought out by this perspective, which we investigate. I will finish by banishing some TQFT myths! This talk is based on joint work with Bruce Bartlett, Chris Schommer-Pries and Chris Douglas.Konrad Waldorf (Regensburg)

**Geometric string structures and supersymmetric sigma models****Abstract:**I describe a simple, finite-dimensional definition of geometric string structures, equivalent to the ones of Stolz and Teichner. Geometric string structures play an important role for the path integral quantization of supersymmetric sigma models, and I try to explain this using recent work of Bunke and a new transgression formula for 2-gerbes.Christoph Wockel (Hamburg)

**A smooth model for the string group****Abstract:**There have been various constructions of the string group out that are suited for differential geometric applications. It cannot be a finite-dimensional Lie group, so one of the most natural things to expect would be an infinite-dimensional Lie group. Surprisingly, such a model did not exist in the past. In this talk we explain how to construct such a model, based on the construction of a topological model by Stolz. Moreover, we show how this can be extended to a Lie 2-group model, making explicit comparisons between ordinary and categorical differential geometry possible.

## Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

How about a link to

Jeffrey Giansiracusa (Bath)

Open closed field theories and deformation theory

his page or even just his e-address?