for this workshop

## Finite tensor categories: their cohomology and geometry

at the

American Institute of Mathematics, Pasadena, California

organized by

Nicolas Andruskiewitsch, Ivan Angiono, Julia Pevtsova, and Julia Plavnik

This workshop, sponsored by AIM and the NSF, will be devoted to the conjecture on finite generation of cohomology for finite tensor categories. This conjecture, stated by Etingof and Ostrik in 2004, has origins in the fundamental results of the cohomology ring a finite group scheme due to Venkov, Evens, Friedlander, Parshall, and Suslin. There have been recent advances both for families of finite dimensional Hopf algebras in zero characteristic whose structure is understood and for finite group schemes over an arbitrary commutative Noetherian base.

The main topics for the workshop are

- Finite generation of cohomology of symmetric tensor categories in positive characteristic.
- Finite generation of cohomology of finite dimensional Hopf algebras and tensor categories.
- Applications of cohomological finite generation to tensor triangular geometry.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*