The purpose of this talk is to introduce locally conformal symplectic manifolds and explain the ideas and main ingredients of the proof of a h-principe for those structures obtained in a joint work with Gael Meigniez.

We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials $\Phi_N$ for the $j$-invariant. These bounds make explicit the best previously known asymptotic bounds. This is joint work with Fabien Pazuki and Florian Breuer.

Numeration 2026 is the 2026 edition of a series of events around numeration systems and substitution systems. The central themes of this conference include (but are not limited to): number theory, diophantine approximation, fractal geometry, substitutions, combinatorics on words, ergodic theory, dynamical systems, and theoretical computer science.

Découvrir le programme
—  Conference website —
https://numeration2026.sciencesconf.org/

— Invited speakers (confirmed) —
Michael Baake, Bielefeld University, Germany
Ayreena Bakhtawar, Polish Academy of Sciences, Poland
Colin Faverjon, University of Picardy Jules Verne, Amiens, France
Lukas Spiegelhofer, Technical University of Leoben, Austria
Manon Stipulanti, University of Liège, Belgium

— Scientific Committee —
– Shigeki Akiyama, University of Tsukuba, Japan
– Valérie Berthé, IRIF, France
– Charlene Kalle, University of Leiden, Netherlands
– Lingmin Liao, University of Wuhan, China
– Edita Pelantová, Czech Technical University, Czech Republic
– Michel Rigo, University of Liège, Belgium
– Wolfgang Steiner, IRIF, France
– Cathy Swaenepoel, University of Paris Cité, France
– Jörg Thuswaldner, Technical University of Leoben, Austria

— Organizing Committee — 
– Cécile Dartyge (IECL, University of Lorraine, France)
– Damien Jamet (LORIA, University of Lorraine, France)
– Manfred Madritsch (Technical University of Leoben, Austria)
– Thomas Stoll (IECL, University of Lorraine, France)

— Past editions —
The previous “Numeration” conferences have been in:
– Tsukuba (2025)
– Utrecht (2024)
– Liège (2023, 2011)
– Vienna (2019)
– Paris (2018)
– Rome (2017)
– Prague (2016, 2008)
– Nancy (2015)
– Debrecen (2014)
– Kyoto (2012)
– Leiden (2010)
– Marseille (2009)
– Graz (2007)
– Grenoble (2005)

We discuss the method of picking a convenient coordinate system adapted to vector fields. Let $X_1, …, X_q$ be either real or complex $C^1$ vector fields. We discuss the question of when there is a coordinate system in which the vector fields are smoother (e.g. $C^m$ or $C^\infty$, or real analytic). By answering this in a quantitative way, we obtain coordinate charts which can be used as generalized scaling maps. When the vector fields are real this is joint work with Stovall, and continues in the line of quantitative sub-Riemannian geometry initiated by Nagel, Stein, and Wainger. When the vector fields are complex one obtains a geometry with more structure which can be thought of as “sub-Hermitian”.

Le miroir d’un entier n dans une  base b donnée est l’entier obtenu en inversant l’ordre  des chiffres de n dans cette base.
Par exemple 31 est le miroir de 13. Dans cet exposé nous montrons qu’il existe une infinité de nombres premiers p dont le miroir dans une base donnée est un entier avec peu de facteurs premiers. Il s’agit d’un travail en commun avec Joël Rivat et Cathy Swaenepoel.