# Higher Structures & Field Theory Seminar

### in brief

biweekly, **Wednesdays 3-5 pm** central European time virtually

### What?

Originally, this seminar on quantum algebra, quantum topology and mathematical physics was supposed to strengthen regional connections by meeting once or twice per semester. However, due to well-known reasons, it will now take place virtually and more regularly instead. It will run biweekly, on Wednesdays at 3-5 pm central European time.- We will start at 3pm with 10 minutes of “virtual tea” for informal converstions, so bring your tea and coffee!
- Then we will have a 50 minute talk, with a 5–10-minute break for discussions after the first half
- Finally, since we are all desperate for some more personal interactions, we will have some time for informal discussions and hopefully many questions after the talk, up to at the latest 5 pm.

### Where?

Of course we will meet virtually! We plan to use Big Blue Button, but reserve to switch to zoom in case of mishaps. More information on connecting can be found here: Technical information for speakersPlease sign up for our

**mailing list**as we will send out the connection information there. (Note that we have to accept your request to avoid spam, so if your email address is not an institutional address or self-explanatory about who you are, please leave your name and institution, or send us a clarifying email.)

### Who?

The speakers in the winter semester 2020/21 are:Nov. 25 | Konrad Waldorf (Greifswald) | ## Connes fusion of spinors on loop spaceI will talk about some progress with the problem to exhibit the 2d supersymmetric sigma model as a smooth and fully extended functorial field theory (FFT), which is part of the Stolz-Teichner programme. The spinor bundle on the loop space of a string manifold is the value of that FFT on circles. I describe a Connes fusion product on this spinor bundle, which produces the assignment of the FFT on a pair of pants, and at the same time gives an ansatz how to extend the FFT down to the point. This work combines operator algebras, infinite-dimensional representation theory and higher-categorical geometry, and is joint with Peter Kristel. |

Dec. 9 | Adrien Brochier (Paris 6) | |

Jan. 13 | Danica Kosanovic (Paris 13) | |

Jan. 27 | Matthias Ludewig (Regensburg) | ## Construction of the supersymmetric path integralThe task of rigorously constructing the path integral for the N=1/2 supersymmetric sigma-model has sparked a lot of research activity in the last 30 years, after it was used by Atiyah to give a short, but formal, proof of the Atiyah-Singer index theorem. In geometric terms, this path integral is just an integration functional for differential forms on the loop space of a spin manifold X, which is, however, ill-defined due to the infinite-dimensionality of the loop space. In this talk, we present a construction of this path integral using cyclic cohomology of the dg algebra of differential forms on X, which is connected to loop space forms via Chen’s iterated integral map. We then explain the connection to path integral formulae using Pfaffians and the Wiener measure. This is joint work with B. Güneysu and F. Hanisch. |

Feb. 10 | |