Everybody is welcome to attend the

Workshop "Fuchsian Differential Equations
in Zero and Positive Characteristic",

Departamento de Matemáticas, Instituto Superior Técnico,

Universidade de Lisboa, Av. Rovisco Pais

Sala 3.10.

February 12 - 16, 2024

UIDB/04459/2020 and UIDP/04459/2020

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

www.xxyyzz.cc/lisboa

www.hh.hauser.cc

An important aspect in the study of Fuchsian differential equations (defined over Q)
is the reduction of the equation modulo a prime p. This concerns in particular the
notorious problem to find criteria which ensure the algebraicity of the solutions,
culminating in the Grothendieck-Katz p-curvature conjecture. Surprisingly, differential
equations defined over a field of characteristic p have not been studied
extensively in the past. Most prominent are papers of Honda, Dwork, and van der Put,
among others, see the bibliography. But already the construction of the exponential
function in positive characteristic as a solution of y' = y seems to have been
overlooked until recently (but see the article of Fürnsinn-Hauser in this respect).

The workshop aims at getting an overview on the existing literature, to study concrete
examples (e.g., classical differential equations as the Airy differential equation),
to investigate the related Galois groups,
and to discuss various algebraicity questions.

Interested people are kindly asked to contact the organizers.

Gregor Böhm, Vienna

Alin Bostan, Paris

Xavier Caruso, Bordeaux

Florian Fürnsinn, Vienna

Nutsa Gegelia, Mainz

Luisa Gietl, Vienna

Herwig Hauser, Vienna

Annette Huber-Klawitter, Freiburg

Hiraku Kawanoue, Chubu

Hadrien Notarantonio, Paris

Eric Pichon, Paris

Duco van Straten, Mainz

Daniel Vargas-Montoya, Toulouse

The workshop will take place at the

Instituto Superior Técnico,

Departamento de Matemáticas, Universidade de Lisboa,
metro Saldanha.

The meeting starts on Monday, February 12, 2024, at 10 am, Sala 3.10.

It ends on Friday, February 16, in the early afternoon.

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.

Honda, T.: Algebraic
differential equations.

Dwork, B.:
Nilpotent p-curvature.

Fürnsinn, F., Hauser, H.:
Fuchsian differential equations in arbitrary characteristic.

Fürnsinn, F., Hauser, H.,
Kawanuoe, H.: On Abel's problem on logarithmic integrals in positive characteristic.

Montoya, D.:
Algebraicity mod p of hypergeometric series.

Montoya, D.:
Algébricité mod p et structure de Frobenius.

Matzat, H., van der Put, M.:
Iterative differential equations.

van der Put, M.:
Differential equations in characteristic p.

van der Put, M.:
Reduction modulo p.

van der Put, M.:
Grothendieck conjecture and Risch equation.

Beukers, F.: Accessory parameters.
Section 2: Considerations modulo p.

Workshop "Periods",

Departamento de Matemáticas, Instituto Superior Técnico,

Universidade de Lisboa,

Sala 3.10.

February 16 - 21, 2023

UIDB/04459/2020 and UIDP/04459/2020

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

www.xxyyzz.cc/lisboa

www.hh.hauser.cc

A ''period'' is the time which elapses until a process comes to the first repetition, which is then repeated over and over again. Pendula, Planetary Trajectories and Wave Functions are classical examples.

In mathematics, periods existed and were described for a long time until Kontsevich and Zagier introduced a precise and comprehensive definition as integrals over semi-algebraic sets defined over Q. Of special interest are the differential equations satisfied by periods, giving rise to many intriguing and fascinating phenomena and questions.

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.

Javier Fresán will give each morning an introductory mini-course. This is then followed by discussions and further presentations over the whole day.

Interested people are kindly asked to contact the organizers.

Alin Bostan, Paris

Javier Fresán, Paris

Florian Fürnsinn, Vienna

Quentin Gazda, Palaiseau

Herwig Hauser, Vienna

Hiraku Kawanoue, Chubu

Hadrien Notarantonio, Saclay

Adolfo Quirós, Madrid

Emre Sertöz, Hannover

Duco van Straten, Mainz

Juan Viu-Sos, Madrid

Sergey Yurkevich, Vienna

The workshop will take place at the

Instituto Superior Técnico,

Departamento de Matemáticas, Universidade de Lisboa,
metro Saldanha.

The meeting starts on Thursday, February 16, 2023, at 10 am, Sala 3.10.

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.

Kontsevich, M., Zagier, D.: Periods.

Fresán, J.: Une introduction aux périodes.

Fresán, J.: Deux exposés sur les périodes (1/2)

Fresán, J.: Deux exposés sur les périodes (2/2)

Cresson, J., Viu-Sos, J.: On the equality of periods of Kontsevich-Zagier.

Waldschmidt, M.: Transcendence of periods: the state of the art.

Waldschmidt, M.: Raconte moi...une période.

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.