Journées du GDR EFI 2022

Europe/Paris
Toulouse

Toulouse

Amphithéâtre Laurent Schwartz, Bat 1R3, UPS
Description

Journées du GDR EFI 2022

Description de la manifestation:

Le GDR EFI a pour but de fédérer les nombreux chercheurs qui travaillent en France dans des domaines dont les équations fonctionnelles sont soit l'objet d'étude soit des outils importants pour les applications. Ces domaines concernent les mathématiques « pures » et « appliquées », l'informatique et la physique théorique. On observe actuellement des interactions de plus en plus fortes entre la théorie et les applications, de nombreuses actions communes ayant eu lieu depuis une dizaine d'années. Par équations fonctionnelles, on entend principalement les équations différentielles ordinaires, aux différences, aux q-différences, mahlériennes, linéaires ou algébriques, éventuellement multivariées. Le cas différentiel algébrique non linéaire concerne par exemple les équations de Painlevé. Tous ces types d'équations fonctionnelles ont été et sont toujours très activement étudiés de nombreux points de vue : algébrique, algorithmique, arithmétique, combinatoire, logique, géométrique, physique, etc.

Les journées du GDR EFI 2022 s'articuleront autour de 2 mini-cours  donnés par Marie Albenque (CNRS et Ecole Polytechnique) et Jason P. Bell (University of Waterloo), ainsi que de 8 exposés courts par Mercedes Haiech, Rémi Jaoui, Mickael Matusinsky, Veronika Pillwein, Jacques Sauloy, Michael Wibmer, Sergey Yurkevich.

Ces journées seront suivies d'une journée d'exposés de recherche de l'ANR De Rerum Natura dont le programme est disponible ici

Registration
Inscription Journées du GDR EFI 2022
Participants
• Alexandre Goyer
• Bruno Salvy
• Charlotte Hardouin
• Colin Faverjon
• Emmanuel PAUL
• Eric Delaygue
• Eric Pichon-Pharabod
• Frederic Jouhet
• Frédéric Chyzak
• Guillaume Rond
• Hadrien Notarantonio
• HUAN DAI
• Jacques Sauloy
• Kilian Raschel
• Marc Mezzarobba
• Marie Albenque
• Mercedes Haiech
• Michael Wibmer
• Mireille Bousquet-Mélou
• Pierre Bonnet
• Remi Jaoui
• Sergey Yurkevich
• Tanguy Rivoal
• Thomas Dreyfus
• Monday, 12 September
• 09:30 10:30
Arithmetic dynamics 1h

We give an introduction to arithmetic dynamics and the questions in the area intended for a broad audience with an emphasis on connections to other branches of mathematics.

Speaker: Jason P. Bell (University of Waterloo)
• 11:00 12:00
Ising model on random planar maps via Tutte’s invariants. 1h

I will present a survey of recent and not so recent results about combinatorial random planar maps decorated (or not !) with a statistical physics model. I will put a special emphasis on the combinatorial aspects of this story. In particular, I will introduce and explain the method of Tutte’s invariants to solve some functional equations.

Speaker: Marie Albenque
• 13:30 14:10
Matzat's conjecture in differential Galois theory 40m

Determining the absolute differential Galois group of interesting differential fields is a central problem in differential Galois theory. For the fields of formal and convergent Laurent series the solution is well-known, but the classical case of rational functions has long resisted a solution. Matzat's conjecture predicts the structure of the absolute differential Galois group of the rational function field, and more generally, of one-variable function fields. In this talk, I will review recent progress towards Matzat's conjecture.

Speaker: Mr Michaël Wibmer ( Home Research Teaching Lise Meitner Grant Michael Wibmer Institute of Analysis and Number Theory Graz University of Technology)
• 14:30 15:10
Hypergeometric diagonals and a step towards Christol's conjecture 40m

Even though diagonals of multivariate rational functions have been studied from various viewpoints, they still remain quite mysterious objects. An example for this is the widely open conjecture by Christol which characterizes diagonals inside the class of all D-finite functions. In 2012 Bostan, Boukraa, Christol, Hassani, and Maillard created a list with 116 potential counter examples for this conjecture. As of today, using new kinds of identities involving diagonals and hypergeometric functions, 40 of these examples were resolved by the starting work of Abdelaziz, Koutschan and Maillard and the generalization by Bostan and the speaker.
In the talk I will explain how the key identities were found and proven, indicate their various implications, and finally mention limitations and possible extensions. The talk is based on joint work with A.~Bostan.

Speaker: Sergey Yurkevich (University Paris-Saclay and University of Vienna)
• 15:30 16:10
The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry 40m

Given a partial differential equation (PDE), its solutions can be difficult, if not impossible, to describe.
The purpose of the Fundamental theorem of tropical (partial) differential algebraic geometry is to extract from the equations certain properties of the solutions.
More precisely, this theorem proves that the support of the solutions in $k[[t_1, \cdots, t_m]]$ (with $k$ a field of characteristic zero) of differential equations can be obtained by solving a so-called tropicalized differential system.

Speaker: Mercedes Haiech (Université de Limoges)
• Tuesday, 13 September
• 09:00 10:00
Ising model on random planar maps via Tutte’s invariants 1h
Speaker: Marie Albenque
• 10:30 11:30
Arithmetic dynamics 1h

We give an introduction to arithmetic dynamics and the questions in the area intended for a broad audience with an emphasis on connections to other branches of mathematics.

Speaker: Prof. Jason P. Bell (University of Waterloo)
• Wednesday, 14 September
• 09:00 10:00
Arithmetic dynamics 1h

We give an introduction to arithmetic dynamics and the questions in the area intended for a broad audience with an emphasis on connections to other branches of mathematics.

Speaker: Mr Jason P. Bell (University of Waterloo)
• 10:30 11:30
Ising model on random planar maps via Tutte’s invariants 1h
Speaker: Marie Albenque