Université de Versailles-St Quentin, Laboratoire de Mathématiques, 45 avenue des États-Unis 78035 Versailles cedex, France
e-mail: divizio[at]math.cnrs.fr          Office: bâtiment Fermat, office 3305


Le groupe de travail «Transcendance et combinatoire» a débuté en janvier 2018. Il bénéficie du soutien de la bourse ERC COMBINEPIC.

Organisateurs : Alin BostanLucia Di Vizio et Kilian Raschel 

Format, lieu et horaires : Le groupe de travail se déroule à l'IHP (11 rue Pierre et Marie Curie 75005 Paris). Il a lieu à raison de deux vendredis par mois, et consiste en deux types de séances, des séances privées de travail et des exposés ouverts au public.  Les exposés sont listés ci-dessous. Certains d'entre eux sont organisés conjointement avec le séminaire POLSYS/MATHEXP, et ont lieu au LIP6 (Sorbonne Université, 4 place Jussieu 75005 Paris).

Pour revoir quelques exposés : c'est par ici... ou sur cette page 


Les annonces des exposés ci-dessous sont diffusés sur la liste  la liste News du GDR EFI : pour s'inscrire (ou se désinscrire) suivre ce lien. Il existe aussi un canal Telegram (https://t.me/gdrefi) et un agenda Google "GDR EFI" (url de l'agendalien ical).

Programme 2022-2023

25/11/2022, 11h (LIP6, 25-26, salle 105) : Christoph Koutschan (RICAM Linz), Guessing with little data [SLIDES]

Reconstructing a hypothetical recurrence equation from the first terms of an infinite sequence is a well-known technique in experimental mathematics, also referred to as "guessing". We combine the classical linear-algebra approach to guessing with lattice reduction, which in many instances allows us to find the desired recurrence using fewer input terms. We have successfully applied our method to sequences from the OEIS and have identified several examples, for which it would have been very difficult to obtain the same result with the traditional approach. This is joint work with Manuel Kauers.

25/11/2022, 14h (LIP6, 25-26, salle 105) : Manuel Kauers (RISC Linz), Gerrymandering [SLIDES]

We report on some efforts to compute the next few terms of the so-called gerrymandering sequence A348456 that counts the number of ways to dissect a square grid into two connected regions of the same size. This is joint work with Christoph Koutschan and George Spahn, arXiv:2209.01787.

25/11/2022, 15h30 (LIP6, 25-26, salle 105): Claudia Fevola (MPI Leipzig), Vector Spaces of Generalized Euler Integrals 

We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated using tools from homological algebra and the theory of D-modules. In this talk, I will present an overview of the main tools needed to study these vector spaces, namely twisted de Rham cohomology and Mellin transform. Finally, I will discuss relations between these approaches. This is a joint project with Daniele Agostini, Anna-Laura Sattelberger, and Simon Telen.

2/12/2022, 14h (IHP, salle 421) : Hadrien Notarantonio (INRIA Saclay), On the algebraicity of solutions of functional equations with one catalytic variable (part II)

Functional equations with one catalytic variable naturally appear in enumerative combinatorics (e.g. when counting planar maps, walks,...). The relevant solution of such an equation is a formal power series with polynomial coefficients in what is called the catalytic variable. Classifying the nature of this solution (e.g. algebraic, D-finite,...) has been an important topic of research since the 60's, starting with the works of Brown and Tutte. In 2006, Bousquet-Mélou and Jehanne obtained a general theorem giving the algebraicity of those solutions. In this talk, I will first briefly reintroduce the combinatorial context and Bousquet-Mélou and Jehanne's result and I will then present links with Artin's approximation theory and Popescu's theorem. I will finally state and prove a recent effective result by Buchacher and Kauers for the algebraicity of the solutions of linear systems of DDEs.

9/12/2022, 14h30 (IHP, amphi Darboux) : Igor Pak (UCLA, Los Angeles), What do we know about the cogrowth sequence?

Take a group and a set of generators. Denote by a(n) the number of words in the generators with product 1 of length n (these are loops in the corresponding Cayley graph). The cogrowth sequence {a(n)} is the main object of our study. Turns out, it carries remarkably rich information about the group, as one considers arithmetic and asymptotic properties of a(n), as well as algebraic properties of the generating function for {a(n)}. In the first half of the talk I will review what is known about the problem from different points of view: combinatorics, group theory and computational complexity. In the second half, I will present our recent work on the subject (joint with David Soukup), where we obtain the first negative result for the cogrowth sequence of nilpotent groups in the most unexpected way. This talk is aimed at the general audience and no background will be assumed.

10/02/2023, 14h (IHP) : Julien Roques (ICJ, Lyon), TBA

Programme 2022-2023 - Séances passées

Programme des années précédentes 

Programme 2021-2022

Programme 2020-2021

Programme 2019-2020

Programme 2018-2019

Programme 2018

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