ALGEBRAIC

MARVELS

IN

DIFFERENTIAL

EQUATIONS

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

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.