Clermont-Darmstadt workshop on the Geometric Satake Equivalence

This workshop was organized in Clermont-Ferrand from Jan. 17th to Jan. 21st, 2022. Our goal was to study the proof of the Geometric Satake Equivalence following a new approach proposed by Fargues-Scholze, which we tried to translate in the more classical world of schemes. The detailed scientific program is available here.

Organizers

Arnaud Mayeux
Timo Richarz
Simon Riche

Notes

Notes corresponding to each talk were written by the speakers:

Talk 0: Introduction and Leitfaden (S. Riche).
Talk 1: Definition of the dual group and the Satake isomorphism (E. Zabeth).
Talk 2: Categories of étale sheaves (C. Mair).
Talk 3: Universally locally acyclic sheaves (P. Bieker).
Talk 4: Relative perverse sheaves (R. Ciloglu).
Talk 5: Hyperbolic localization (A. Mayeux).
Talk 6: Affine Grassmannians (A. Güthge).
Talk 7: Beilinson-Drinfeld Grassmannians (Y. El Kaouni).
Talk 8: Semi-infinite orbits (S. Riche).
Talk 8.5: Technique talk on the formalism of equivariant sheaves (T. Richarz).
Talk 9: Definition of the Satake category and convolution (T. Wedhorn).
Talk 10: Constant term functors and tensor structures (T. Van Den Hove).
Talk 11: Tannakian reconstruction (C. Yaylali).
Talk 12: Identification of the dual group (T. Richarz).

Any comments are welcome!

Schedule

Monday, Jan. 17th, 2022

8.25-8.45: Introduction and Leitfaden (S. Riche).
8.45-10.10: Talk 1 (E. Zabeth).
10.10-10.30: Coffee break.
10.30-12: Talk 2 (C. Mair).
12-14: Lunch.
14-15.30: Talk 3 (P. Bieker).

Tuesday, Jan. 18th, 2022

8.45-10.10: Talk 4 (R. Ciloglu).
10.10-10.30: Coffee break.
10.30-12: Talk 5 (A. Mayeux).
12-14: Lunch.
14-15.30: Talk 6 (A. Güthge).

Wednesday, Jan. 19th, 2022

8.45-10.10: Talk 7 (Y. El Kaouni).
10.10-10.30: Coffee break.
10.30-12: Talk 8 (S. Riche).
12-14: Lunch.
Walk in the afternoon.

Thursday, Jan. 20th, 2022

9-10: Talk 8.5 (T. Richarz).
10-10.30: Coffee break.
10.30-12: Talk 9 (T. Wedhorn).
12-14: Lunch.
14-15.30: Talk 10 (T. Van Den Hove).

Friday, Jan. 21st, 2022

8.45-10.10: Talk 11 (C. Yaylali).
10.10-10.30: Coffee break.
10.30-12: Talk 12 (T. Richarz).
12-14: Lunch.

Participants

Alexandre Astruc (École Normale Supérieure de Lyon)
Pierre Baumann (Université de Strasbourg)
Patrick Bieker (Technische Universität Darmstadt)
Rizacan Ciloglu (Technische Universität Darmstadt)
Yassine El Kaouni (Technische Universität Darmstadt)
Arthur Garnier (Université de Picardie Jules Verne)
Stéphane Gaussent (Université Jean Monnet - Saint-Étienne)
Anton Guethge (Technische Universität Darmstadt)
Daniel Juteau (Université de Picardie Jules Verne)
Catrin Mair (Technische Universität Darmstadt)
Leonardo Maltoni (Sorbonne Université)
Arnaud Mayeux (Université Clermont Auvergne)
Timo Richarz (Technische Universität Darmstadt)
Simon Riche (Université Clermont Auvergne)
Thibaud Van Den Hove (Technische Universität Darmstadt)
Torsten Wedhorn (Technische Universität Darmstadt)
Can Yaylali (Technische Universität Darmstadt)
Emilien Zabeth (Université Clermont Auvergne)

Funding

This event is funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 101002592).