ETHZ-UZh-Sbg Arithmetic and Geometry Research Group

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Workshop "Alpbach 2017: Arithmetic Algebraic Geometry"

This workshop is organized by J. Ayoub, C. Fuchs, A. Kresch, R. Pink and G. Wüstholz. The workshop takes place from July 9 - July 15, 2017 at the Böglerhof in Alpbach/Tyrol, Austria.

This, the 11th in a series of Workshops in Alpbach, will feature minicourses and invited talks on topics covering a spectrum of modern arithmetic geometry. Minicourses presenting a broad overview of these topics, delivered by top international experts, will be complemented by invited talks highlighting recent progress.

Poster: JPG

The group picture with the workshop participants can be found here: JPG

Participants:
Joseph Ayoub (U. Zurich)
Olivier Benoist (Strasbourg)
Yohan Brunebarbe (U. Zurich)
Brian Conrad (Stanford)
Yoël Dadoun (U. Zurich)
Javier Fresán (ETH Zurich)
Clemens Fuchs (U. Salzburg)
Sergey Gorchinskiy (Steklov Inst., Moscow)
Fritz Hörmann (U. Freiburg)
Ariyan Javanpeykar (Mainz)
Dimitar Jetchev (EPFL)
Peter Jossen (ETH Zurich)
Rafael von Känel (Princeton U.)
Christina Karolus (U. Salzburg)
Lars Kühne (U. Basel)
Andrew Kresch (U. Zurich)
Maxim Mornev (Leiden U.)
Alberto Navarro (U. Zurich)
Jacob Oesinghaus (U. Zurich)
Richard Pink (ETH Zurich)
Samir Siksek (Warwick)
Ruiran Sun (Mainz)
Yunqing Tang (IAS)
Gisbert Wüstholz (ETH Zurich)
Wei Zhang (Columbia)
The participants consist of PhD students and postdocs in arithmetic and geometry from Zurich as well as colleagues from Basel, Freiburg, Lausanne, Leiden, Mainz, Moscow, Princeton, Salzburg, and Strasbourg.

Minicourses:
Brian Conrad: Pseudo-reductive groups: structure theory and arithmetic applications
Samir Siksek: Galois representations of elliptic curves and Diophantine applications
Wei Zhang: Shtukas and higher Gross-Zagier formula

Program:
The program will start on Sunday evening, the first talk (given by D. Jetchev) is scheduled for 17:15-18:45. The detailed program (including abstracts) will be announced here; it includes confirmed minicourses by Brian Conrad, Samir Siksek and Wei Zhang as well as invited talks by J. Fresán, A. Javanpeykar, D. Jetchev and Yunqing Tang: Program-2017

Sunday, 09.07.2017 (Arrival day): Arithmetic properties of special cycles on unitary Shimura varieties (welcome talk given by Dimitar Jetchev)
Monday: Shtukas and higher Gross-Zagier formula. I (Wei Zhang); Galois representations of elliptic curves and Diophantine applications. I (Samir Siksek); Pseudo-reductive groups: structure theory and arithmetic applications. I (Brian Conrad)
Tuesday: Galois representations of elliptic curves and Diophantine applications. II (Samir Siksek); Pseudo-reductive groups: structure theory and arithmetic applications. II (Brian Conrad); Exponential motives (Javier Fresán); Arithmetic, algebraic, and analytic hyperbolicity (Ariyan Javanpeykar); Exceptional splitting of reductions of abelian surfaces with real multiplication (Yunqing Tang)
Wednesday: Galois representations of elliptic curves and Diophantine applications. III (Samir Siksek); Shtukas and higher Gross-Zagier formula. II (Wei Zhang)
Possible afternoon program: Informal discussion, excursions, hiking tours.
Thursday: Shtukas and higher Gross-Zagier formula. III (Wei Zhang); Pseudo-reductive groups: structure theory and arithmetic applications. III (Brian Conrad); Galois representations of elliptic curves and Diophantine applications. IV (Samir Siksek)
Friday, 14.07.2017: Pseudo-reductive groups: structure theory and arithmetic applications. IV (Brian Conrad); Shtukas and higher Gross-Zagier formula. IV (Wei Zhang)

Schedule:
09:00 - 10:30: Minicourse lecture
10:30 - 11:00: Coffee break
11:00 - 12:30: Minicourse lecture
12:45: Lunch
13:45 - 15:15: Minicourse 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
18:00 - 19:00: Invited talk
19:00: Dinner

Lecture Notes and Literature:
Background material related to Brian Conrad's minicourse: Linear algebraic groups: course 1, course 2 (Note: only sections 1 and 2 of course 2); Weil restriction (affine case is enough): Section 7.6 of the book Neron Models (PDF). Familiarity with Borel's textbook "Linear Algebraic Groups" up through 14.11 in Chap. IV is also sufficient.
Further references will be announced here.
Impressum    14.07.2017