A seminar on Topological and Geometrical Structures of Information has been organized at CIRM in 2017, to gather engineers, applied and pure mathematicians interested in the geometry of information. This year FGSI’19 conference will be focused on the foundations of geometric structures of information. It is dedicated to the triumvirat Cartan - Koszul - Souriau and their influence on the field.

Poster

For the 50th birthday of Jean-Marie Souriau Book “Structure des systèmes dynamiques” published in 1969, and Jean-Louis Koszul Book Translation by Springer “Introduction to Symplectic Geometry”, FGSI’19 will celebrate the influence of the Triumvirate Elie Cartan (ENS, 1888), Jean-Louis Koszul (ENS, 1940) and Jean-Marie Souriau (ENS, 1942) on Foundations of Geometric Structure of Information. Both Koszul and Souriau were influenced by Elie Cartan works on symmetric homogeneous spaces. Jean-Louis Koszul has developed theory of hessian geometry introducing Koszul forms that are fundamental structures in Information Geometry. In parallel Souriau has developed in the framework of Geometrical Mechanics applied for Statistical Mechanics, a Lie Group Thermodynamics in Homogeneous Symplectic Manifold. Based on Souriau cocycle, this thermodynamics defines a generalized Fisher metric where the Gibbs Maximum Entropy density is covariant with respect to dynamic groups of Physics.

Elie Cartan started his carreer at Montpellier, where he was appointed in 1894 as lecturer in mathematics and assistant professor of astronomy at the Faculty of Sciences of Montpellier. We can read in one letter: “*Je fus nommé maître de conférences à Montpellier. Je garde le meilleur souvenir que j'ai passé en province, à Montpellier d'abord. Ce furent des années de méditation dans le calme, et tout ce que j'ai fait plus tard est contenu en germe dans mes travaux murement médités de cette période. **[I was appointed lecturer at Montpellier. I keep the best memory I have spent in the province, in Montpellier first. It was years of calm meditation, and everything I did later is germinating in my meditated works of that period.]*»

FGSI’19 workshop will federate researchers and Engineers coming from Pure/Applied Mathematics, Geometrical Mechanics and Statistical Physics and Information Theory, to explore new foundations of Geometric Science of Information based on structures emerging from Koszul and Souriau works.

Interview of Jean-Louis Koszul

Interview of Jean-Marie Souriau

**Related conferences:**

On the occasion of the 50th birthday of J-M Souriau's book Structure des Systèmes Dynamiques, another conference in honnor of J-M Souriau will be organized in Paris-Diderot university at 27-31 May 2019 : souriau2019.fr

The 63th SOURIAU COLLOQUIUM will be held from June 30th to July 5th 2019 in the historical city of Arpino, 100 kilometers south east of Rome, in Italy.

http://www.memocsevents.eu/wordpress/cossevita/souriau-colloquium/

**GSI’19 “Geometric Science of Information”** : www.gsi2019.com

**CIMI Labex Trimester “Statistics with Geometry & Topology”**: https://perso.math.univ-toulouse.fr/statistics-geometry-and-topology/