ETHZ-UZh-Sbg Arithmetic and Geometry Research Group
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Workshop "Alpbach 2023"
This workshop is organized by J. Ayoub, C. Fuchs, P. Habegger, R. Pink, and S. Zerbes. The workshop takes place from June 25-30, 2023 at the Böglerhof in Alpbach/Tyrol, Austria.
This, the 16th in a series of Workshops in Alpbach, will feature minicourses given by world class researchers and invited talks by younger researchers, covering topics in arithmetic geometry related to Galois representations and heights. 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.
The group picture with the workshop participants can be found here: JPG
Participants:
Joseph Ayoub (U. Zurich)
Ran Azouri (U. Paris-Nord)
Yohan Brunebarbe (U. Bordeaux)
Alina Bucur (UCSD)
Alessio Cangini (U. Basel)
Neeraj Deshmukh (U. Zurich)
Gabriel Dill (U. Hannover)
Marta Dujella (U. Basel)
Clemens Fuchs (U. Salzburg)
Tim Gehrunger (ETH Zurich)
Philipp Habegger (U. Basel)
Rafael von Känel (Tsinghua U.)
Kiran Kedlaya (UCSD)
Bruno Klingler (HU Berlin)
Dmitrii Krekov (ETH Zurich)
Andrew Kresch (U. Zurich)
Holly Krieger (U. Cambridge)
Maxim Mornev (EPFL)
Yilin Ni (ETH Zurich)
Richard Pink (ETH Zurich)
Gerold Schefer (U. Basel)
Johannes Schmitt (U. Zurich)
Julia Schneider (EPFL)
Felix Sefzig (U. Zurich)
Ana Vego (ETH Zurich)
Wojtek Wawrow (UCL)
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:
Kiran Kedlaya: Galois representations and Fargues-Fontaine curves
Bruno Klingler: Hodge theory, between algebraicity and transcendence
Holly Krieger: Heights, equidistribution, and arithmetic dynamics
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 Kiran Kedlaya, Bruno Klingler and Holly Krieger as well as invited talks by Yohan Brunebarbe, Tim Gehrunger, Julia Schneider and Rafael von Känel.

Sunday, 25.06.2023 (Arrival day): Counting D4 quartic extensions of a number field ordered by discriminant (Alina Bucur)
Monday: Galois representations and Fargues-Fontaine curves. I (Kiran Kedlaya); Hodge theory, between algebraicity and transcendence. I (Bruno Klingler); Counting integral points on varieties with large fundamental group (Yohan Brunebarbe)
Tuesday: Heights, equidistribution, and arithmetic dynamics. I (Holly Krieger); Galois representations and Fargues-Fontaine curves. II (Kiran Kedlaya); The stable (marked) reduction of hyperelliptic curves (Tim Gehrunger)
Wednesday: Hodge theory, between algebraicity and transcendence. II (Bruno Klingler); Heights, equidistribution, and arithmetic dynamics. II (Holly Krieger); Heights, equidistribution, and arithmetic dynamics. III (Holly Krieger)
Thursday: Galois representations and Fargues-Fontaine curves. III (Kiran Kedlaya); Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank (Julia Schneider)
Possible afternoon program: Informal discussion, excursions, hiking tours.
Friday, 30.06.2022 (Departure day): Hodge theory, between algebraicity and transcendence. III (Bruno Klingler); Integral points on coarse Hilbert moduli schemes (Rafael von Känel)

Schedule:
09:00 - 10:30: Lecture
10:30 - 11:00: Coffee break
11:00 - 12:30: Lecture
12:45: Lunch
13:45 - 15:15: Lecture
15:15 - 18:00: Time for informal discussion
18:30: Dinner
Lecture Notes and Literature:
K. Kedlaya: Sheaves, stacks, and shtukas, Lecture Notes from the Arizona Winter School, 2017 (published in DOI). Preprint available online at PDF.
K. Kedlaya: Perfectoid spaces: an annotated bibliography, ICTS, Bengaluru, 2019 (published in DOI). Preprint available online at PDF.
K. Kedlaya: New methods for (\phi,\Gamma)-modules, Research in the Mathematical Sciences 2:20 (2015): PDF, Errata
Further references will be announced here.
Impressum    03.07.2023