Certaines caractéristiques de la dynamique sont lisibles au travers des propriétés géométriques de l'espace des configurations:
->  quelles propriétés dynamiques et/ou statistiques sont cachées dans ce paysage géométrique?
->  comment explorer de tels paysages?

10h00   Marco Pettini   (Osservatorio Astrofisico di Arcetri, Firenze)
Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
11h20   Frédéric Cazals   (INRIA Sophia-Antipolis)
Protein folding: energy landscapes, spectral analysis, and Morse theory

Résumé du séminaire de M. Pettini

This talk surveys some aspects relating two basic topics in physics: Hamiltonian dynamics, mainly for what concerns chaotic instability, and statistical mechanics, mainly for what concerns phase transition phenomena in systems described by realistic interatomic or intermolecular forces. The geometrization of Hamiltonian dynamics (where natural motions are identified with geodesics of appropriately defined Riemannian manifolds) makes possible to "read" in the geometry of these mechanical manifolds relevant properties of the dynamics.
The first part of the talk contains what we can call the beginning of a Riemannian theory of the origin of the chaotic instability of Hamiltonian dynamics. The second part of the talk stems from another question, again rooted in the Riemannian theory of chaos: what happens to these mechanical manifolds when a Hamiltonian system undergoes a phase transition? and how can we "geometrically read" the occurrence of a phase transition? It is at this point that topology comes into play, and, considering certain submanifolds of configuration space, the answer is that necessarily a phase transition can occur only at a point where the topology of these submanifolds undergoes a transition, and this is true at least for a large class of systems. It is therefore natural to consider the corresponding distribution of the (Morse) critical points.
Apart from the conceptual relevance of this approach, it is of prospective interest to the study of transitional phenomena - for instance - in finite, small N systems, in disordered and amorphous materials, in polymers and proteins.

Résumé du séminaire de F. Cazals

This talk will overview three topics related to the question of understanding protein folding. First, we shall review some core concepts involved in the latest models revolving around energy landscapes. Second, we shall bridge the gap between folding and the (spectral) analysis of point clouds sampling such landscapes --a point cloud being generated by a molecular dynamics simulation of a folding process. Finally, we shall argue that a more local analysis of sampled landscapes should be undertaken, and as a proof of concept, we shall present a Morse theory based algorithm to reconstruct non manifold shapes from sample points in the 3D Euclidean space.