Workshop Lisboa February 2020:

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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


    Topic

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.

    Participants

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

    Practical information

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.

    Reading material

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,

Open Format

Open Format 2019:

Open Format 2019:

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 & Orlando Neto


    Topics

Algebraic solutions of differential equations;

reduction modulo p;

monodromy group;

Picard-Fuchs equations;

regular singular points;

Malgrange index theorem;

Bernstein-Sato polynomial;

    Participants

Alin Bostan

Eric Delaygue

Herwig Hauser

Orlando Neto

Julien Roques

Duco van Straten

Fernando Rodriguez Villegas

Michael Wibmer

    Practical information

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.

    Reading Material

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),


    Contact

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.

Open Format 2018:

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 & Orlando Neto

    Topics

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.

    Participants

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.

    Practical information

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.

    Reading Material

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.

    Contact

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.