Algebraicity and Transcendence for Singular Differential Equations

The format of this two-weeks event is audience-oriented: Instead of having a sequel of very specialized talks on the speaker's own favorite research theme we plan to design a list of topics and techniques of general interest from which the participants can learn in order to enrich and facilitate their own work. In this spirit, speakers are asked to prepare material suggested by the organizers (but of course coordinated with them) and to present it in an accessible manner enabling a deeper understanding of the main aspects.

The first week will be more in "Summer School Style", with four mini-courses (four sessions each), complemented by working and exercise sessions in small groups. This week should be valuable for both students and senior researchers.

The second week will be more "Conference Style", but again emphasizing the dialogue and allowing for discussions during the presentations.

The theme of the program "Algebraicity and Transcendence for Singular Differential Equations" represents a rich source of phenomena, techniques, problems, ranging from analysis to algebra, number theory and combinatorics, often based on and stimulated by experimental material and long-ranging conjectures. We are looking forward to have an exciting event.

Oct. 7, 2024
09:00 — 09:30
Registration & Welcome
09:30 — 10:45
Julien Roques (Institute Camille Jordan, U Lyon)
The p-Curvature Conjecture, I
11:00 — 12:45
13:00 — 14:00
Lunch Break
14:00 — 15:00
15:00 — 15:30
Coffee Break
15:30 — 16:45
Oct. 8, 2024
09:00 — 10:45
Daniel Vargas-Montoya (IMT, Toulouse)
A p-adic Approach to Differential Equations, II
11:00 — 12:45
13:00 — 14:30
Lunch Break
14:30 — 15:30
Julien Roques (U of Lyon)

Problem Session

15:30 — 16:00
Coffee Break
16:00 — 16:45
Michael Singer (North Carolina State U, Raleigh)

Problem Session

Oct. 9, 2024
09:00 — 10:45
11:00 — 12:45
Julien Roques (Institute Camille Jordan, U Lyon)
The p-Curvature Conjecture, II
13:00 — 14:30
Lunch Break
14:30 — 15:30
Daniel Vargas-Montoya (IMT, Toulouse) & Masha Vlasenko (KSE, Kyiv)

Problem Session

15:30 — 16:00
Coffee Break
16:00 — 16:45
Duco van Straten (U of Mainz)

Problem Session

Oct. 10, 2024
09:00 — 10:45
11:00 — 12:45
13:00 — 14:30
Lunch Break
14:30 — 15:30
Michael Singer (North Carolina State U, Raleigh)

Problem Session

15:30 — 16:00
Coffee Break
16:00 — 16:45
Julien Roques (U of Lyon)

Problem Session

17:00 — 17:45
Daniel Vargas-Montoya (IMT, Toulouse) & Masha Vlasenko (KSE, Kyiv)

Problem Session in the Common Room

Oct. 11, 2024
09:00 — 10:45
Julien Roques (Institute Camille Jordan, U Lyon)
The p-Curvature Conjecture, III
11:00 — 12:45
13:00 — 14:30
Lunch Break
14:30 — 15:30
Duco van Straten (U of Mainz)

Problem Session

15:30 — 16:00
Coffee Break & Farewell
Oct. 14, 2024
09:00 — 09:30
Registration & Welcome
09:30 — 12:15
Javier Fresán (Sorbonne U, Paris)
On G-functions of differential order 2
12:15 — 14:00
Lunch Break
14:00 — 15:15
Yoshishige Haraoka (Josai University)
Higher dimensional Katz theory
15:15 — 15:30
Coffee Break
15:30 — 16:45
Oct. 15, 2024
11:00 — 12:15
Hiraku Kawanoue (Chubu U, Kasugai City)
The exponential function in characteristic p
12:15 — 14:00
Lunch Break
15:15 — 15:30
Coffee Break
Oct. 16, 2024
11:00 — 12:15
12:15 — 14:00
Lunch Break
15:00 — 16:15
Vesselin Dimitrov (Caltech)
Arithmetic holonomy bounds

via zoom

Oct. 17, 2024
11:00 — 12:15
Éric Delaygue (Institute Camille Jordan, U Lyon)
On Abel's problem and Gauss congruences
12:15 — 14:00
Lunch Break
15:15 — 15:30
Coffee Break
15:30 — 16:45
Vasily Golyshev (Abdus Salam ICTP)
Beyond Complex Multiplication
Oct. 18, 2024
09:00 — 10:15
12:15 — 14:30
Lunch Break

Organizers

Name Affiliation
Alin Bostan INRIA Paris
Francis Brown University of Oxford
Herwig Hauser University of Vienna
Shihoko Ishii University of Tokyo
Hiraku Kawanoue Chubu University
Michael Singer North Carolina State University

Attendees

Name Affiliation
Hiroki Aoki Tokyo University of Science
Matthias Aschenbrenner University of Vienna
Vincent Bagayoko Université Paris Cité
Frits Beukers Utrecht University
Gregor Böhm University of Vienna
Jean-Benoît Bost University Paris Sud
Manfred Buchacher Johannes Kepler Universität
Francisco Castro Universidad de Sevilla
Christopher Chiu Katholieke Universiteit Leuven
Gilles Christol Université de Jussieu
Éric Delaygue Institute Camille Jordan
Vesselin Dimitrov Caltech University
Roland Donninger University of Vienna
Sebastian Eterovic University of Leeds
Eleonore Faber University of Graz
Javier Fresán Sorbonne University
Florian Fürnsinn University of Vienna
Francisco García Cortés Universidad de Sevilla
Nutsa Gegelia Johannes-Gutenberg Universität Mainz
Vasily Golyshev Abdus Salam International Centre for Theoretial Physics
Anna Goncharuk Karazin Kharkiv National University
Sebastian Gontarek University of Wroclaw
Davide Guzzetti SISSA
Yoshishige Haraoka Josai University
Charlotte Hardouin Institut de Mathématiques de Toulouse
Zhiqiang He CNRS - Université Grenoble Alpes
Martin Kalck University of Graz
Manuel Kauers Johannes Kepler Universität
Maxim Kontsevich Institut des Hautes Etudes Scientifiques
Christoph Koutschan Johann Radon Institute for Computational and Applied Mathematics
Christian Krattenthaler University of Vienna
Abhiram Mamandur Kidambi Max Planck Institute for Mathematics in the Sciences
Anton Mellit University of Vienna
Luis Narváez Macarro Universidad de Sevilla
Adele Padgett University of Vienna
Eric Pichon Max Planck Institute for Mathematics in the Sciences
Andrea Pulita Université Grenoble Alpes
Nigel Pynn-Coates University of Vienna
Feliks Rączka Institute of Mathematics of the Polish Academy of Sciences
Armin Rainer University of Vienna
Julien Roques Institute Camille Jordan
Bruno Salvy Inria Lyon
Josef Schicho Johannes Kepler Universität
Michael Schlosser University of Vienna
Szilárd Szabó Eötvös Loránd University Budapest
Yunqing Tang California Institute of Technology
Marius van der Put University of Groningen
Duco van Straten Johannes-Gutenberg Universität Mainz
Daniel Vargas-Montoya Institut de Mathématiques de Toulouse
Masha Vlasenko Kyiv School of Economics
Shoji Yokura Kagoshima University
Masaaki Yoshida Fukuoka University
Masahiko Yoshinaga Osaka University
Sergey Yurkevich University of Vienna
Wadim Zudilin Radboud University
Preview of Michael Singer - Differential Galois Theory and the Algebraicity of Solutions, I
Michael Singer (NC State U, Raleigh): Differential Galois Theory and the Algebraicity of Solutions, I
Oct. 7, 2024 11:00 — 12:45
Preview of Duco van Straten - Differential Equations, Geometry and Arithmetic, I
Duco van Straten (U Mainz): Differential Equations, Geometry and Arithmetic, I
Oct. 7, 2024 14:00 — 15:00
Preview of Masha Vlasenko - A p-adic Approach to Differential Equations, I
Masha Vlasenko (KSE, Kyiv): A p-adic Approach to Differential Equations, I
Oct. 7, 2024 15:30 — 16:45
Preview of Daniel Vargas-Montoya - A p-adic Approach to Differential Equations, II
Daniel Vargas-Montoya (IMT, Toulouse): A p-adic Approach to Differential Equations, II
Oct. 8, 2024 09:00 — 10:45
Preview of Duco van Straten - Differential Equations, Geometry and Arithmetic, II
Duco van Straten (U Mainz): Differential Equations, Geometry and Arithmetic, II
Oct. 8, 2024 11:00 — 12:45
Preview of Michael Singer - Differential Galois Theory and the Algebraicity of Solutions, II
Michael Singer (NC State U, Raleigh): Differential Galois Theory and the Algebraicity of Solutions, II
Oct. 9, 2024 09:00 — 10:45
Preview of Duco van Straten - Differential Equations, Geometry and Arithmetic, III
Duco van Straten (U Mainz): Differential Equations, Geometry and Arithmetic,III
Oct. 10, 2024 09:00 — 10:45
Preview of Michael Singer - Differential Galois Theory and the Algebraicity of Solutions, III
Michael Singer (NC State U, Raleigh): Differential Galois Theory and the Algebraicity of Solutions, III
Oct. 11, 2024 11:00 — 12:45
Preview of Javier Fresán - On G-functions of differential order 2
Javier Fresán (Sorbonne U, Paris): On G-functions of differential order 2
Oct. 14, 2024 09:30 — 12:15
Preview of Yoshishige Haraoka - Higher dimensional Katz theory
Yoshishige Haraoka (Josai University): Higher dimensional Katz theory
Oct. 14, 2024 14:00 — 15:15
Preview of Andrea Pulita - p-adic differential equations over Berkovich curves
Andrea Pulita (U Grenoble Alpes): p-adic differential equations over Berkovich curves
Oct. 14, 2024 15:30 — 16:45
Preview of Maxim Kontsevich - On Katz' nilpotence conjecture, p-determinants, and q-generalization
Maxim Kontsevich (IHES, Bures-sur-Yvette): On Katz' nilpotence conjecture, p-determinants, and q-generalization
Oct. 16, 2024 11:00 — 12:15
Preview of Éric Delaygue - On Abel's problem and Gauss congruences
Éric Delaygue (Institute Camille Jordan, U Lyon): On Abel's problem and Gauss congruences
Oct. 17, 2024 11:00 — 12:15
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 01
Herwig Hauser - Fuchsian Differential Equations, Part 01
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 02
Herwig Hauser - Fuchsian Differential Equations, Part 02
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 03
Herwig Hauser - Fuchsian Differential Equations, Part 03
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 04
Herwig Hauser - Fuchsian Differential Equations, Part 04
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 05
Herwig Hauser - Fuchsian Differential Equations, Part 05
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 06
Herwig Hauser - Fuchsian Differential Equations, Part 06
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 07
Herwig Hauser - Fuchsian Differential Equations, Part 07
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 08
Herwig Hauser - Fuchsian Differential Equations, Part 08
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 09
Herwig Hauser - Fuchsian Differential Equations, Part 09
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 10
Herwig Hauser - Fuchsian Differential Equations, Part 10
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 11
Herwig Hauser - Fuchsian Differential Equations, Part 11
Preview of Herwig Hauser - Fuchsian Differential Equations, Part 12
Herwig Hauser - Fuchsian Differential Equations, Part 12
Preview of Herwig Hauser - Fuchsian Differential Equations, Trailer
Herwig Hauser - Fuchsian Differential Equations, Trailer
At a glance
Type:
Workshop
When:
Oct. 7, 2024 — Oct. 18, 2024
Where:
ESI Boltzmann Lecture Hall
Organizer(s):
Alin Bostan (INRIA Paris)
Francis Brown (U Oxford)
Herwig Hauser (U of Vienna)
Shihoko Ishii (U Tokyo)
Hiraku Kawanoue (Chubu U, Kasugai City)
Michael Singer (NC State U, Raleigh)
More:
Website