ETHZ-UZh-Sbg Arithmetic and Geometry Research Group
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Workshop "Alpbach 2022"
This workshop is organized by J. Ayoub, C. Fuchs, P. Habegger, R. Pink, G. Wüstholz, and Sarah Zerbes. The workshop takes place from June 26-July 1, 2022 at the Böglerhof in Alpbach/Tyrol, Austria.
This, the 15th 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. Zurich)
Ana Caraiani (Imperial C. London)
Baptiste Depouilly (ETH Zurich)
Neeraj Deshmukh (U. Zurich)
Marta Dujella (Basel)
Clemens Fuchs (U. Salzburg)
Ziyang Gao (U. Hannover)
Tim Gehrunger (ETZ Zurich)
Philipp Habegger (Basel)
Urs Hartl (U. Münster)
Bence Hevesi (UCL)
Emil Jacobsen (U. Zurich)
Andrew Kresch (U. Zurich)
Lars Kühne (U. Hannover)
Alexander Kutzim (U. Münster)
Maximilian Langner (U. Münster)
David Loeffler (Warwick)
Maxim Mornev (EPFL)
Richard Pink (ETH Zurich)
Zhenlin Ran (U. of Newcastle)
Gerold Schefer (Basel)
Felix Sefzig (U. Zurich)
Robert Wilms (Basel)
Gisbert Wüstholz (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, Hannover, London, Münster and Salzburg among others.
Minicourses:
Ana Caraiani: Cohomolgy of Shimura varieties
Philipp Habegger: The Schinzel-Zassenhaus Conjecture and Arithmetic Dynamics
Urs Hartl: Shtukas for function fields
(Tentative) 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 Ana Caraiani, Philipp Habegger and Urs Hartl as well as invited talks by Ziyang Gao, Lars Kühne, Zhenlin Ran and Robert Wilms.

Sunday, 26.06.2022: Arrival day
Monday: The Schinzel-Zassenhaus Conjecture and Arithmetic Dynamics. I (Philipp Habegger); Cohomology of Shimura varieties. I (Ana Caraiani); Heights and singular moduli of Drinfeld modules (Zhenlin Ran)
Tuesday: Cohomology of Shimura varieties. II (Ana Caraiani); The Schinzel-Zassenhaus Conjecture and Arithmetic Dynamics. II (Philipp Habegger); Torsion points in families of abelian varieties (Ziyang Gao)
Wednesday: The Schinzel-Zassenhaus Conjecture and Arithmetic Dynamics. III (Philipp Habegger); Cohomology of Shimura varieties. III (Ana Caraiani); Shtukas for function fields. I (Urs Hartl)
Thursday: Shtukas for function fields. II (Urs Hartl); On the irreducibility of arithmetic divisors (Robert Wilms)
Possible afternoon program: Informal discussion, excursions, hiking tours.
Friday, 01.07.2022 (departure day): Shtukas for function fields. III (Urs Hartl); The Relative Bogomolov Conjecture for Fibered Products of Elliptic Families (Lars Kühne)

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:
Potential automorphy over CM fields (ten author paper including Ana Caraiani): arXiv:1812.09999
An example-based introduction to Shimura varieties (by Kai-Wen Lan): URL
Lower bounds for the canonical height of a unicritical polynomial and capacity (by Ph. Habegger and H. Schmidt): arXiv:2111.01870
A proof of the Schinzel-Zassenhaus conjecture on plolynomials (by Vesselin Dimitrov): arXiv:1912.12545
Further references will be announced here.
Impressum    30.06.2022