This, the 19th in a series of Workshops in Alpbach, will feature minicourses given by world class researchers and invited talks by younger researchers, covering topics in various areas of number theory, including but not limited to arithmetic geometry, Galois representations, etc. The emphasis includes not only deep theoretical developments, but also applications of a more concrete/computational nature. Minicourses presenting a broad overview of these topics, delivered by top international experts, will be complemented by invited talks highlighting recent progress.
Participants:
Shabnam Akhtari (Penn State U.)
Joseph Ayoub (U. Zurich)
Tobias Bisan (U. Basel)
Alessio Cangini (U. Basel)
Simone Coccia (U. Basel)
Hymn Chan (U. Toronto)
Pierre Colmez (IMJ-PRG)
Hang Fu (U. Basel)
Clemens Fuchs (U. Salzburg)
Tim Gehrunger (ETH Zurich)
Alexandros Groutides (U. Warwick)
Philipp Habegger (U. Basel)
Florian Herzig (U. Toronto)
Tobias Hilgart (U. Salzburg)
Samuel Huber (ETH Zurich)
Thomas Jacob (U. Zurich)
Dmitrii Krekov (ETH Zurich)
David Loeffler (FernUni Schweiz)
Francesco Naccarato (ETH Zurich)
Wieslawa Niziol (IMJ-PRG)
Richard Pink (ETH Zurich)
Simon Pitte (ENS Lyon)
Carina Premstaller (U. Salzburg)
Nischay Reddy (U. Toronto)
Gabriel Ribeiro (ETH Zurich)
Janine Roshardt (ETH Zurich)
Alois Schaffler (FernUni Schweiz)
Miriam Schönauer (U. Salzburg)
Linli Shi (ETH Zurich & FernUni Schweiz)
Ana Marija Vego (ETH Zurich)
Jianfeng Xie (ETH Zurich)
Sarah Zerbes (ETH Zurich)
Beat Zurbuchen (ETH Zurich)
The participants consist of PhD students and postdocs in arithmetic and geometry from Zurich as well as colleagues from Basel and Salzburg among others.
Minicourses:
Pierre Colmez and Wieslawa Niziol (IMJ-PRG):
Hodge theory of p-adic varieties
Shabnam Akhtari (Penn State U.):
Reduction theory of integral binary forms and counting in number fields
Florian Herzig (U. Toronto):
Mod-p cohomology for GL_2
Program:
The program will start on Sunday evening, the first talk is scheduled for 17:15-18:45. The detailed program (including abstracts)
can be found here:
PDF; it includes confirmed minicourses by Pierre Colmez and Wieslawa Niziol, Shabnam Akhtari, and Florian Herzig, as well as invited talks by Simone Coccia, Hymn Chan, Gabriel Ribeiro, Janine Roshardt, and Linli Shi.
| Sunday, 14.06.2026 (Arrival day): Hodge theory of p-adic varieties. I (Pierre Colmez and Wieslawa Niziol) |
| Monday: Reduction theory of integral binary forms and counting in number fields. I (Shabnam Akhtari); Mod-p cohomology for GL_2. I (Florian Herzig); Density of integral points on character varities (Simone Coccia); Wach modules of crystalline (phi,Gamma)-modules over the Robba ring (Janine Roshardt) |
| Tuesday: Hodge theory of p-adic varieties. II (Pierre Colmez and Wieslawa Niziol), Reduction theory of integral binary forms and counting in number fields. II (Shabnam Akhtari); Modularity in Higher Chow Groups and Beilinson's Conjecture (Linli Shi) |
Wednesday: Mod-p cohomology for GL_2. II (Florian Herzig); Hodge theory of p-adic varieties. III (Pierre Colmez and Wieslawa Niziol)
Possible afternoon program: Informal discussion, excursions, hiking tours.
|
| Thursday: Reduction theory of integral binary forms and counting in number fields. III (Shabnam Akhtari); Mod-p cohomology for GL_2. III (Florian Herzig); Hodge theory of p-adic varieties. IV (Pierre Colmez and Wieslawa Niziol)
|
| Friday, 19.06.2026 (Departure day): On Breuil's Lattice Conjecture for GL_2 (Hymn Chan); Smooth coefficient systems (Gabriel Ribeiro) |
Schedule:
09:00 - 10:30: Lecture
10:30 - 11:00: Coffee break
11:00 - 12:30: Lecture
or
09:00 - 10:00: Invited talk
10:00 - 10:30: Coffee break
10:30 - 11:30: Invited talk
12:30: Lunch
13:45 - 15:15: Lecture
15:15 - 18:00: Time for informal discussion
or
13:45 - 14:45: Invited talk
15:00 - 16:00: Invited talk
16:00 - 18:00: Time for informal discussion
19:00: Dinner
Lecture Notes and Literature:
Further references will be announced here.