Open Format:

ALGEBRAIC
AND
ANALYTIC
ASPECTS
OF
POWER
SERIES

CMAF-CIO, FCUL, SALA 6.2.33, UNIVERSIDADE DE LISBOA,

JANUARY 26 - 31, 2018

Website: www.xxyyzz.cc

Organized by: Herwig Hauser & Orlando Neto

Perspective

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.