Special day in honor of Paulo Ribenboim
Institut Henri Poincaré - Amphi Hermite
On the occasion of his 90th birthday
20 Mars 2018
11, rue Pierre et Marie Curie 75005 PARIS
10:45 - 11:30 Lou van den Dries:
Hardy fields, transseries, and surreal numbers
This is about joint work with Matthias Aschenbrenner and Joris van der Hoeven. I will discuss how the three topics in the title are related.
Partly this is still conjectural. Valuation theory as in
Paulo's Theorie des Valuations plays an important role in dealing
with these structures.
11:45 - 12:30 Franziska Jahnke:
Definable Henselian Valuations
Although the study of the definability of henselian valuations has a long history starting with J. Robinson, most of the results in this area were proven during the last few years. We survey a number of these results which address the definability of concrete henselian valuations, the existence of definable henselian valuations on a given field, and questions of uniformity and quantifier complexity.
Lunch 12:30 -14:30
14:30 - 15:15 Sibylla Priess-Crampe:
Asymptotic approximations - a short insight into my joint work with
Paulo for our book on Ultrametric Spaces
A strictly contracting mapping from a spherically complete ultrametric space
into itself has a unique fixed point. This fixed point can be approximated
by a family of elements which are determined by the mapping. We will show
how this general method can be applied to the case of ordinary differential
equations of polynomial type over Hardy fields.
15:30 - 16:15 Paulo Ribenboim:
Roots of Polynomials in Ultranormed Rings
Coffee and tea break 16:15 - 17:00
17:00 - 17:45 Daniel Bertrand:
Pell equations over polynomial rings
Interest in these equations goes back to Abel. I will describe the new
development brought by Masser and Zannier in the case of square free
discriminants, in relation with their work on unlikely intersections in
abelian schemes. The case of non separable discriminants leads to
similar problems on generalized jacobians, where unexpected solutions
sometimes appear. I will also discuss generalized Pell equations and
their link with relative versions of the Mordell-Lang problem.
Birthday cocktail 18:00 - 20:00
This event is supported by IMJ-PRG,
Projets Logique and Théorie
des nombres, and by
Organizers: Zoé Chatzidakis, Françoise Delon, Max
Dickmann, Danielle Gondard and Tamara Servi.