Workshop "Arithmetic of Differential Equations",

Centro de Matemática e Aplicações Fundamentais (CMAF-CIO),

Faculdade de Ciências, Universidade de Lisboa,

Sala 6.2.33.

February 17 - 21, 2020

www.xxyyzz.cc

Contact: Herwig Hauser, University of Vienna

www.hh.hauser.cc

We wish to investigate circumstances where the solutions of (naturally given) ordinary differential
equations have integer coefficients.

We start from Zagier's paper "Arithmetic and Topology of
Differential Equations" and try to understand some of its features.

We will then look at various examples (Apéry's recursion, hypergeometric equation,...).

Often, one observes that the solution has integral coefficients or, at least, coefficients of moderate
convergence/divergence.

The reason for this, however, remains a mystery.

Alin Bostan, Paris

Orlando Neto, Lisbon

Jean-Marie Maillard, Paris

Duco van Straten, Mainz

Julien Roques, Lyon

Sergey Yurkevich, Vienna

Paul Zellhofer, Vienna

Carlos Florentino, Lisbon

Anton Mellit, Vienna

Herwig Hauser, Vienna

The workshop will take place at the

Centro de Matemática e Aplicações Fundamentais da Universidade de Lisboa, sala 6.2.33,

situated on the ground floor of
pavillon C6 (Faculdade de Ciências) of the campus, metro Cidade Universitária.

The meeting starts on Monday, February 17,
at 10 am.

Students and interested researchers are very welcome;

They are kindly asked to contact the organizers in advance.

Supported in part by the Austrian Science Fund FWF through project P-31338.

We are very grateful for the kind hospitality offered by the mathematicians at the Universidade de Lisboa.

Zagier: Arithmetic and Topology of
Differential Equations,

Zagier: Integral solutions,

Beukers: Consequences of Apéry's work,

Beukers & Peters: K3 Surfaces and zeta(3),

Beukers: Accessory parameters,

Beukers: Irrationality & modular forms,

Beukers: Hypergeometric functions,

Yurkevich-Zellhofer: Basics,

Dan Li: Periods,

Paule-Radu: Algorithms for modular forms,

ALGEBRAIC

MARVELS

IN

DIFFERENTIAL

EQUATIONS

Departamento de Matematicas,

CMAF-CIO, FCUL, Sala 6.2.33, Universidade de Lisboa,

February 18 - 22, 2019

Website: www.xxyyzz.cc

Organized by: Herwig Hauser

Algebraic solutions of differential equations;

reduction modulo p;

monodromy group;

Picard-Fuchs equations;

regular singular points;

Malgrange index theorem;

Bernstein-Sato polynomial;

Alin Bostan

Eric Delaygue

Herwig Hauser

Orlando Neto

Julien Roques

Duco van Straten

Fernando Rodriguez Villegas

Michael Wibmer

The workshop will take place at the

Departamento de Matematicas da Universidade
de Lisboa, sala 6.2.33.

It is situated on the ground floor of
pavillon C6 (Faculdade de Ciencias) of the UL campus, metro Cidade Universitária.

The meeting starts on Monday, February 17, at 10 am.

Students and interested researchers are very welcome

to attend the workshop; they are kindly asked

to contact the organizers in advance.

Bostan Linz I,

Bostan Linz II,

Bostan Linz III,

Bostan Linz IV,
Bostan Linz V,

Honda (D-finite),

André (Gevrey series),

Maillet (Gevrey solutions),

Roques (diff. Galois theory),

Singer (difference equations),

Adamczewski-Bell-Delaygue (alg. independence),

Wibmer (diff. Galois theory),

Herwig Hauser, Faculty of Mathematics, University of Vienna, Austria

www.hh.hauser.cc,

herwig.hauser@univie.ac.at.

Orlando Neto, Departamento de Matematicas da Universidade
de Lisboa

orlando60@gmail.com

Supported in part by the Austrian Science Fund FWF through project P-31338.

We are grateful for the kind hospitality of the Department of Mathematics at the Universidade de Lisboa.

ALGEBRAIC

AND

ANALYTIC

ASPECTS

OF

POWER

SERIES

Departamento de Matematicas, Universidade de Lisboa,

January 26 - 31, 2018

Website: www.xxyyzz.cc

Organized by: Herwig Hauser

Numerous exciting results circle around the quality of specific power series:

formal, convergent, algebraic, Gevrey, Mahler, D-finite, P-recursive,
differentially algebraic, holonomic, hypergeometric, lacunary, G-functions, ..., with often sharp contrasts between characteristic zero and
positive characteristic.

For all these there are intriguing examples, counter-examples, particularities, results, techniques, comparisons, algorithms,
computations, conjectures. We wish to get a more precise view on all this material in order to focus on particularly interesting
problems and phenomena. The goal would be to design a prospective roadmap for future research and activities.

Boris Adamczewski,

Mariemi Alonso,

Alin Bostan,

Francisco Castro-Jiménez,

Eric Delaygue,

Herwig Hauser,

Luis Narváez,

Orlando Neto,

Julien Roques,

Duco van Straten,

Michael Wibmer,

... as well as local mathematicians and students.

The workshop will take place at the Departamento de Matematicas da Universidade de Lisboa, sala 6.2.33. It is situated on the ground floor of
pavillon C6 of the campus, metro Cidade Universitária.

The meeting starts on Saturday, January 27, at 10 am.
Students and interested researchers are very welcome to attend the discussions; they are kindly asked to contact the organizers in advance.

Sharif-Woodcock (diagonals),

Eisenstein / Heine (denominators),

Denef-Lipshitz (diagonals),

Furstenberg (diagonals),

Adamczewski-Bell (alg. series),

Bostan Linz I,

Bostan Linz II,

Bostan Linz III,

Bostan Linz IV,

Bostan Linz V,

Polya (entire series),

Honda (D-finite),

André (Gevrey series),

Mahler (Minkowski),

Mahler (lacunary),

Banderier-Drmota (survey),

Christol (diagonals),

Dwork-van der Poorten (Eisenstein constant),

Hickel-Matusinski (algebraic Puiseux series),

Kedlaya (alg. series char. p),

Lafon (Weierstrass alg. series),

Matsuda (alg. solutions diff. equ.),

Dreyfus-Hardouin-Roques (hypertranscendance),

Maillet (Gevrey solutions),

Samol-van Straten,

Roques (diff. Galois theory),

Singer (difference equations),

Hardouin-Singer,

Adamczewski-Bell-Delaygue (alg. independence),

Wibmer (diff. Galois theory),

... to be continued.

Herwig Hauser, Faculty of Mathematics, University of Vienna, Austria

www.hh.hauser.cc,

herwig.hauser@univie.ac.at.

Supported in part by the Austrian Science Fund FWF through project P-25652.

We are grateful for the kind hospitality of the Department of Mathematics at the Universidade de Lisboa.