Syllabus

In 1969 the groundbreaking book of Jean-Marie Souriau appeared, Structure des systèmes dynamiques. We will celebrate, in 2019, the jubilee of its publication, with a conference in honour of the work of this great scientist.

The influence of Souriau’s work is felt in the areas he has innovated or developed in his own way. It is important to take stock of it, in particular in order to make the current and future generations aware of his original and deep thought.

The main reasons for organising this conference are the singularity, and at the same time the scope, of the work of Souriau. He was able to create, in his time, a homogeneous group of “Souristes” who for the most part have reached maturity and are able today to convey the originality of this work. It is also time to take stock of the important work to which it has given rise among foreign researchers, many of whom we will invite to speak. The work of Jean-Marie Souriau lives on in different areas of the scientific world and, at different levels of depth, in the development of mathematics and physics, and therefore according to the different temporalities of the history of these disciplines.

All scholars, old and new, recognize this. Souriau’s work is particularly important work for the relationships he has established and developed between physics and geometry. He is one of the most important founders of symplectic geometry, and the theoretical exploitation of his work in this field is far from exhausted.

André Lichnerowicz has said that his work could belong to four international scientific unions: mathematics, mechanics, physics and astronomy. But what interests us is not only Souriau the scientist, but also the philosopher. What is striking is the unity of his thought through the variety of his fields of interest. It is likely true that this thought grows deeper as its areas of application expand. The object of our inquiry will be to analyse his thought insofar as it is related to the philosophy of science and even to pure philosophy.

This conference aims to review the entire work of Jean-Marie Souriau in the five areas in which he worked.

  1. Symplectic mechanics. Symplectic structure of the space of the movements of a dynamic system, action of invariance groups, moment map, symplectic cohomology, barycentric decomposition theorem. Elementary systems (particles): homogeneous symplectic variety, classification by coadjoint orbits.

  2. Geometric Quantization. Prequantization condition, pre-quantum bundle, polarizations, quantification of coadjoint orbits.

  3. Thermodynamics. Geometric statistical equilibria in symplectic manifolds. Vector temperature and thermodynamic dissipative model in general relativity.

  4. General Relativity and Cosmology. General Covariance Principle, Robertson-Walker universe model with cosmological constant.

  5. Diffeology. Renewal of the formal framework of differential geometry by a stable space category by all natural set operations (i.e. complete, complete, Cartesian closed). This includes highly singular spaces that may not even be separated, infinite dimensional spaces, and so on.

  6. Philosophy of Science, Epistemology, History of Science. History of each of the domains evoked (symplectic mechanics, quantification, cosmology and relativity, thermodynamics). In each of these areas Souriau introduced new ideas. These new views have not ceased to be relevant and fruitful. The task of a philosophy of science will be to highlight this novelty.

As far as philosophy is concerned, a new question has been raised about the importance of this work, in its variety and unity, and in its impact on the philosophy of science and philosophy in general, which we propose to deal with in this conference. Souriau’s originality manifested itself in his will and in his attempts to create new languages. We will analyze, in the philosophy section, this important aspect of his work, most evident in his work in geometry and relativity.


Organisers: J.-J. Szczeciniarz, P. Iglesias-Zemmour, G. Catren, M. Lachieze-Rey  
Scientific committee: D. Bennequin & A. Weinstein. 
Sponsors: Séminaire de Physique Mathématique, APC & SPHERE (Université Paris-Diderot), UMR 7373 CNRS (I2M, Aix-Marseille Université), LIA «Identities, Forces, Quanta» (CNRS & Universidad CAECE).