ETHZ-UZh-Sbg Arithmetic and Geometry Research Group

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**Workshop "Alpbach 2018: Galois Representations and Heights"**

This workshop is organized by J. Ayoub, C. Fuchs, R. Pink and G. Wüstholz. The workshop takes place from July 1 - July 6, 2018 at the Böglerhof in Alpbach/Tyrol, Austria.

This, the 12th 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.

**Participants:**

Joseph Ayoub (U. Zurich)

Jennifer Balakrishnan (Boston U.)

Iuliya Beloshapka (ETH Zurich)

Olivier Benoist (Strasbourg)

Yohan Brunebarbe (U. Zurich)

Yoel Dadoun (U. Zurich)

Gabriel Dill (U. Basel)

Linda Frey (U. Basel)

Clemens Fuchs (U. Salzburg)

Ziyang Gao (IMJ-PRG)

Sergey Gorchinskiy (Steklov Math. Inst., NRU HSE, Moscow)

Peter Gräf (U. Heidelberg)

Jennifer-Jayne Jakob (ETH Zurich)

Peter Jossen (ETH Zurich)

Ernst Kani (Queen's U. at Kingston)

Christina Karolus (U. Salzburg)

Dmitry Krekov (NRU HSE, Moscow)

Andrew Kresch (U. Zurich)

Nikolas Kuhn (Stanford)

Denis Levchenko (U. Zurich)

Keerthi Madapusi Pera (Boston College)

Alberto Merici (U. Zurich)

Maxim Mornev (ETH Zurich)

Nicolas Müller (ETH Zurich)

Alberto Navarro (U. Zurich)

Joachim Petit (U. Basel)

Richard Pink (ETH Zurich)

Alexandre Puttick (ETH Zurich)

Paul Steinmann (ETH Zurich)

Jack Thorne (U. Cambridge)

Gisbert Wüstholz (ETH Zurich)

Volker Ziegler (U. Salzburg)

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:**

Jennifer Balakrishnan:*Quadratic Chabauty*

Jack Thorne:*Modularity over imaginary quadratic fields*

Keerthi Madapusi Pera:*Heights of abelian varieties with complex multiplication*

**(Tentative) Program:**

The program will start on Sunday evening, the first talk (given by E. Kani) is scheduled for 17:15-18:45. The detailed program (including abstracts) will be announced here; it includes confirmed minicourses by Jennifer Balakrishnan, Jack Thorne and Keerthi Madapusi Pera as well as invited talks by Olivier Benoist, Y. Brunebarbe and S. Gorchinskiy: Program-2018

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

19:00: Dinner

**Lecture Notes and Literature:**

Further references will be announced here.

Back to the main page.

This workshop is organized by J. Ayoub, C. Fuchs, R. Pink and G. Wüstholz. The workshop takes place from July 1 - July 6, 2018 at the Böglerhof in Alpbach/Tyrol, Austria.

This, the 12th 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.

Joseph Ayoub (U. Zurich)

Jennifer Balakrishnan (Boston U.)

Iuliya Beloshapka (ETH Zurich)

Olivier Benoist (Strasbourg)

Yohan Brunebarbe (U. Zurich)

Yoel Dadoun (U. Zurich)

Gabriel Dill (U. Basel)

Linda Frey (U. Basel)

Clemens Fuchs (U. Salzburg)

Ziyang Gao (IMJ-PRG)

Sergey Gorchinskiy (Steklov Math. Inst., NRU HSE, Moscow)

Peter Gräf (U. Heidelberg)

Jennifer-Jayne Jakob (ETH Zurich)

Peter Jossen (ETH Zurich)

Ernst Kani (Queen's U. at Kingston)

Christina Karolus (U. Salzburg)

Dmitry Krekov (NRU HSE, Moscow)

Andrew Kresch (U. Zurich)

Nikolas Kuhn (Stanford)

Denis Levchenko (U. Zurich)

Keerthi Madapusi Pera (Boston College)

Alberto Merici (U. Zurich)

Maxim Mornev (ETH Zurich)

Nicolas Müller (ETH Zurich)

Alberto Navarro (U. Zurich)

Joachim Petit (U. Basel)

Richard Pink (ETH Zurich)

Alexandre Puttick (ETH Zurich)

Paul Steinmann (ETH Zurich)

Jack Thorne (U. Cambridge)

Gisbert Wüstholz (ETH Zurich)

Volker Ziegler (U. Salzburg)

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.

Jennifer Balakrishnan:

Jack Thorne:

Keerthi Madapusi Pera:

The program will start on Sunday evening, the first talk (given by E. Kani) is scheduled for 17:15-18:45. The detailed program (including abstracts) will be announced here; it includes confirmed minicourses by Jennifer Balakrishnan, Jack Thorne and Keerthi Madapusi Pera as well as invited talks by Olivier Benoist, Y. Brunebarbe and S. Gorchinskiy: Program-2018

Sunday, 01.07.2018 (Arrival day): Moduli problems associated to isomorphisms of elliptic Galois representations (welcome talk given by Ernst Kani) |

Monday: Modularity over imaginary quadratic fields. I (Jack Thorne); Quadratic Chabauty. I (Jennifer Balakrishnan); Heights of abelian varieties with complex multiplication. I (Keerthi Madapusi Pera) |

Tuesday: Modularity over imaginary quadratic fields. II (Jack Thorne); Quadratic Chabauty. II (Jennifer Balakrishnan); A real period-index theorem (Olivier Benoist); Hyperbolicity of moduli spaces of Calabi-Yau varieties with level structure (Yohan Brunebarbe) |

Wednesday: Heights of abelian varieties with complex multiplication. II (Keerthi Madapusi Pera); Quadratic Chabauty. III (Jennifer Balakrishnan) Possible afternoon program: Informal discussion, excursions, hiking tours. |

Thursday: Modularity over imaginary quadratic fields. III (Jack Thorne); Heights of abelian varities with complex multiplication. III (Keerthi Madapusi Pera); Relative Milnor K-groups and differential forms of split nilpotent extensions (Sergey Gorchinskiy) |

Friday, 06.07.2018: Heights of abelian varities with complex multiplication. IV (Keerthi Madapusi Pera); Modularity over imaginary quadratic fields. IV (Jack Thorne) |

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

19:00: Dinner

Further references will be announced here.

Impressum 29.06.2018