Topological Aspects of Quantum Field Theories with Chris Schommer-Pries and Peter Teichner
June 13th - June 19th, 2016
Participants at the 2016 workshop
The second European Talbot workshop took place in Germany from June 13 to June 19, 2016. The goal was 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 were given by the participants, with enough free time in the afternoon and evenings for further discussions and interaction. The character of the workshop was 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 have to created an informal and inspiring atmosphere.
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.
Monday: Arrival day
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)
9:30-Classical and Quantum Dijkgraaf-Witten theory (Chern-Simons for finite groups)
11-Dualizability and 1D TFTs
14-2D TFTs and Frobenius Algebras
9:30- Comparison of some models of 2-categories
11-(Symmetric monoidal) Bicategories, Examples: Morita bicategory, bordism
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
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
The application dealine has now passed.
The local expenses for all participants will be covered by the workshop, in particular the costs for accommodation and meals.
For questions or suggestions, please send an email to the organizers email@example.com.
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.