**Topological aspects of quantum field theories**

Winterberg, Germany

June 13th – June 19th, 2016

**About**

The second European Talbot workshop will take place in Germany from June 13 to June 19, 2016. The goal is to bring together a group of 25-30 graduate students and post-docs to work on a focused topic under the guidance of two senior mentors.

Most of the talks will be given by the participants, with enough free time in the afternoon and evenings for further discussions and interaction. The character of the workshop is expository in nature, starting with the basic ideas and leading to a survey of the most recent developments in the field. Since all participants will stay together at a Chalet, jointly responsible for cooking and cleaning, we hope to create an informal and inspiring atmosphere.

**Topic**

The topic of this years’ workshop is topological field theories and their interaction with homotopy theory and mathematical physics, and it will be mentored by Chris Schommer-Pries and Peter Teichner.

In recent years, the interplay between geometric topology, homotopy theory, and theoretical physics has played a significant role in the mathematics of quantum field theory. One of the unifying developments is the theory of higher categories which has turned out to be perfectly suited to the study of various problems, for example that of field theories, especially with regard to matters of locality. It is also a catalyst for many interactions with homotopy theory.

This workshop will be centered around mathematical aspects of quantum field theory, with the aim for participants to reach the frontier knowledge as quickly as possible. These aspects include: Origins of topological quantum field theory in physics, e.g., quantum mechanics and Chern–Simons theory, a mathematical formalism for field theories as functors on geometric bordism categories, and de Rham cohomology and K-theory from super symmetric field theories. We will also discuss fully local (extended) field theories, higher categories and the cobordism hypothesis as well as applications to low dimensional classifications and relations with tensor categories.

**Schedule**

Monday: Arrival day

Tuesday:

10:30-Introduction by Mentors

12-Classical Field Theories, Action Functionals, Examples

15-Quantization in Quantum Mechanics, Wiener measure

17-From Path Integrals to Functorial Field Theories (Example of FFT: Euler theory)

Wednesday

9:30-Classical and Quantum Dijkgraaf-Witten theory (Chern-Simons for finite groups)

11-Dualizability and 1D TFTs

14-2D TFTs and Frobenius Algebras

Thursday:

9:30- Comparison of some models of 2-categories

11-(Symmetric monoidal) Bicategories, Examples: Morita bicategory, bordism

14-Excursion

Friday:

9:30-(0,1,2) Classification and comparison to 2D TFTs Part 1

11-(0,1,2) Classification and comparison to 2D TFTs Part 2

14-(1,2,3) TFTs and Quantum groups Part 1

16-(1,2,3) TFTs and Quantum groups Part 2

Saturday:

9:30-K-theory, Bott periodicity, and Field theories Part 1

11-K-theory, Bott periodicity, and Field theories Part 2

14-Finite Chern-Simons as a fully extended theory

16-Future directions by Mentors

**Application**

The application deadline has passed. Decisions will be made shortly.

**Funding**

The local expenses for all participants will be covered by the workshop, in particular the costs for accommodation and meals.

**Contact**

For questions or suggestions, please send an email to the organizers [email protected].

This workshop is organized by Tobias Barthel, Amalie Høgenhaven, Magdalena Kedziorek, and Sean Tilson, and its concept has been inspired by the US Talbot workshop. We gratefully acknowledge funding and support from Max Planck Institute for Mathematics, and the Laboratory for topology and neuroscience of the EPFL.