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

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.

Brian Conrad's personal notes: PDF

Further references will be announced here.

Back to the main page.

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

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.

Brian Conrad:

Samir Siksek:

Wei Zhang:

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

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.

Brian Conrad's personal notes: PDF

Further references will be announced here.

Impressum 24.07.2017