BIREP summer school on finite tensor categories 2025

This summer school will explore finite tensor categories, a subject of great interest in recent years that has developed into a vibrant area of research with deep connections across pure mathematics. In particular, they have found profound connections to representation theory. Despite the ongoing efforts to fully understand these categories, several aspects of the theory remain open, posing interesting challenges. Among the unresolved questions are important conjectures about the cohomological finite generation of finite tensor categories. Additionally, finite tensor categories play a central role in the advancement of non-commutative tensor triangular geometry, further highlighting their relevance in mathematics.

Beyond their connections to representation theory, finite tensor categories have found interactions with commutative algebra and equivariant algebraic topology, particularly through the study of Betti numbers in this context. These conjectures and open problems not only deepen our understanding of the structure of tensor categories but also offer potential insights into broader mathematical frameworks.

Date: August 4–August 8, 2025

Location: DEULA Westerstede

Invited speaker: Julia Plavnik (Bloomington, USA)

Registration Deadline: June 1, 2025

Organisers: Raphael Bennett-Tennenhaus, Benedikt Fluhr, Juan Omar Gomez, and Chris J. Parker

We aim to bring together 20–25 graduate students and early-career postdocs to explore a specific topic under the guidance of a senior mentor. The majority of the talks will be given by participants and will be expository in nature, providing essential tools to navigate recent developments and open questions in the area. Each participant will have the opportunity to choose a topic from the list of talks they are comfortable with. This way everyone will teach others and learn from others.

Funding

The summer school is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via the the TRR 358 "Integral Structures in Geometry and Representation Theory" (SFB-TRR 358/1 2023 – 491392403).

We will cover accommodation and meals for all participants. However, we strongly encourage participants to seek their own travel funding.

Contact

If you have any questions about the summer school, please contact the organisers at birep-school.