ETHZ-UZh-Sbg Arithmetic and Geometry Research Group

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**Workshop "Alpbach 2021"**

This workshop is organized by J. Ayoub, C. Fuchs, P. Habegger, R. Pink, and G. Wüstholz. The workshop takes place from September 5-10, 2021 at the Böglerhof in Alpbach/Tyrol, Austria.

This, the 14th 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)

Jean-Benoit Bost (U. Paris-Saclay)

Reda Boumasmoud (IMJ-PRG)

Francois Charles (U. Paris-Saclay)

Baptiste Depouilly (ETH Zurich)

Gabriel Dill (Oxford)

Marta Dujella (U. Basel)

Ziyang Gao (IMJ-PRG)

Tim Gehrunger (ETH Zurich)

Philipp Habegger (U. Basel)

Emil Jacobsen (U. Zurich)

Andrew Kresch (U. Zurich)

Lars Kühne (U. Copenhagen)

Denis Levchenko (U. Zurich)

David Loeffler (Warwick)

Lorenzo Mantovani (U. Zurich)

Alberto Merici (U. Zurich)

Maxim Mornev (ETH Zurich)

Nicolas Müller (ETH Zurich)

Richard Pink (ETH Zurich)

Gerold Schefer (U. Basel)

Felix Sefzig (ETH Zurich)

Wojtek Wawrow (London SGNT)

Gisbert Wüstholz (ETH Zurich)

Sarah Zerbes (UCL)

The participants consist of PhD students and postdocs in arithmetic and geometry from Zurich as well as colleagues from Basel, Moscow and Salzburg among others.

**Minicourses:**

Jean-Benoit Bost and Francois Charles:*Infinite-dimensional geometry of numbers and Diophantine applications*

David Loeffler and Sarah Zerbes:*Euler systems and the Bloch-Kato conjecture*

Ziyang Gao and Lars Kühne:*The uniform Mordell-Lang conjecture*

**Program:**

The program will start on Monday morning, the first talk is scheduled for 9:00-10:30. The detailed program (including abstracts) can be found here: PDF; it includes confirmed minicourses by Jean-Benoit Bost and Francois Charles, by David Loeffler and Sarah Zerbes and by Ziyang Gao and Lars Kühne as well as invited talks by Reda Boumasmoud, Gabriel Dill and Lorenzo Mantovani.

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: Invited talk

15:15 - 18:00: Time for informal discussion

19:00: Dinner

**Lecture Notes and Literature:**

References can be found in the program.

Back to the main page.

This workshop is organized by J. Ayoub, C. Fuchs, P. Habegger, R. Pink, and G. Wüstholz. The workshop takes place from September 5-10, 2021 at the Böglerhof in Alpbach/Tyrol, Austria.

This, the 14th 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

Joseph Ayoub (U. Zurich)

Jean-Benoit Bost (U. Paris-Saclay)

Reda Boumasmoud (IMJ-PRG)

Francois Charles (U. Paris-Saclay)

Baptiste Depouilly (ETH Zurich)

Gabriel Dill (Oxford)

Marta Dujella (U. Basel)

Ziyang Gao (IMJ-PRG)

Tim Gehrunger (ETH Zurich)

Philipp Habegger (U. Basel)

Emil Jacobsen (U. Zurich)

Andrew Kresch (U. Zurich)

Lars Kühne (U. Copenhagen)

Denis Levchenko (U. Zurich)

David Loeffler (Warwick)

Lorenzo Mantovani (U. Zurich)

Alberto Merici (U. Zurich)

Maxim Mornev (ETH Zurich)

Nicolas Müller (ETH Zurich)

Richard Pink (ETH Zurich)

Gerold Schefer (U. Basel)

Felix Sefzig (ETH Zurich)

Wojtek Wawrow (London SGNT)

Gisbert Wüstholz (ETH Zurich)

Sarah Zerbes (UCL)

The participants consist of PhD students and postdocs in arithmetic and geometry from Zurich as well as colleagues from Basel, Moscow and Salzburg among others.

Jean-Benoit Bost and Francois Charles:

David Loeffler and Sarah Zerbes:

Ziyang Gao and Lars Kühne:

The program will start on Monday morning, the first talk is scheduled for 9:00-10:30. The detailed program (including abstracts) can be found here: PDF; it includes confirmed minicourses by Jean-Benoit Bost and Francois Charles, by David Loeffler and Sarah Zerbes and by Ziyang Gao and Lars Kühne as well as invited talks by Reda Boumasmoud, Gabriel Dill and Lorenzo Mantovani.

Sunday, 05.09.2021 (Arrival day) |

Monday: Infinite-dimensional geometry of numbers and Diophantine applications. I (Jean-Benoit Bost); Euler systems and the Bloch-Kato conjecture. I (David Loeffler); U-operators and Seed relations (Reda Boumasmoud) |

Tuesday: Euler systems and the Bloch-Kato conjecture. II (Sarah Zerbes); Infinite-dimensional geometry of numbers and Diophantine applications. II (Francois Charles); Distinguished categories and the Zilber-Pink conjecture (Gabriel Dill) |

Wednesday: The uniform Mordell-Lang conjecture. I (Ziyang Gao) and II (Lars Kühne) Possible afternoon program: Informal discussion, excursions, hiking tours. |

Thursday: Infinite-dimensional geometry of numbers and Diophantine applications. III (Francois Charles); Euler systems and the Bloch-Kato conjecture. III (Sarah Zerbes); On the Chow-Witt ring of the moduli stacks of genus one curves (Lorenzo Mantovani) |

Friday, 10.09.2021: Euler systems and the Bloch-Kato conjecture. IV (David Loeffler); Infinite-dimensional geometry of numbers and Diophantine applications. IV (Jean-Benoit Bost) |

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: Invited talk

15:15 - 18:00: Time for informal discussion

19:00: Dinner

References can be found in the program.

Impressum 10.09.2021