Workshop "Fuchsian Differential Equations",

Departamento de Matemáticas, Instituto Superior Técnico,

Universidade de Lisboa,

Sala 3.10.

May 11 - 15, 2022

Contact: Herwig Hauser, Faculty of Mathematics, University of Vienna

www.xxyyzz.cc

www.hh.hauser.cc

Fuchsian Differential Equations are ordinary linear equations typically with polynomial
coefficients. As such they are susceptible to algebraic and arithmetic methods.

For instance, their behaviour under reduction modulo a prime p is still full of mysteries and
unsolved conjectures.

We will approach the topic in a very accessible and explicit manner, looking at concrete examples,
computational aspects, various conjectures, and a comparison of main techniques.

Interested people are kindly asked to contact the organizers.

Alin Bostan, Paris

Frits Beukers, Utrecht

Xavier Caruso, Bordeaux

Duco van Straten, Mainz

Julien Roques, Lyon

Josef Schicho, Linz

Sergey Yurkevich, Vienna

Florian Fürnsinn, Vienna

Cazibe Kavalci, Ankara

Raphaël Pagès, Bordeaux

Orlando Neto, Lisbon

Carlos Florentino, Lisbon

Giancarlo Cotti, Lisbon

Herwig Hauser, Vienna

The workshop will take place at the

Instituto Superior Técnico,

Departamento de Matemáticas, Universidade de Lisboa,
metro Saldanha.

The meeting starts on Wednesday, May 11, at 9 am.

Students and interested researchers are very welcome;

Supported in part by the Austrian Science Fund FWF through project P-34576.

We are very grateful for the kind hospitality offered by the mathematicians at the
Instituto Superior Técnico of Universidade de Lisboa,
especially José Mourão and João Pimentel.

André: p-curvature conjecture

Chambert-Loir: Algébricité

Chudnovsky's: Padé approximation and p-curvature

Cormier et al: Differential operators and minimal polynomial

Calegari, Dimitrov, Tang: Unbounded denominators

Foucault: Picard Fuchs equations and hyperelliptic curves

Foucault, Toffin: Kodaira–Spencer map

Katz: p-curvature conjecture, Bull SMF

Katz: p-curvature conjecture, Inventiones

Kontsevich: Noncommutative identities

Singer: Algebraic solutions

van der Put: Differential equations characteristic p

Chambert-Loir: Algébricité

Chudnovsky's: Padé approximation and p-curvature

Cormier et al: Differential operators and minimal polynomial

Calegari, Dimitrov, Tang: Unbounded denominators

Foucault: Picard Fuchs equations and hyperelliptic curves

Foucault, Toffin: Kodaira–Spencer map

Katz: p-curvature conjecture, Bull SMF

Katz: p-curvature conjecture, Inventiones

Kontsevich: Noncommutative identities

Singer: Algebraic solutions

van der Put: Differential equations characteristic p

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.