Finding saddle points of energy landscapes: why and how?

Orateur: Tony Lelièvre
Localisation: ,
Type: Colloquium de Créteil
Site: UPEC
Salle: Amphi 8 - Auditorium de la MSE
Date de début: 21/12/2023 - 13:45
Date de fin: 21/12/2023 - 14:45

The motivation of this presentation comes from the analysis of metastable stochastic process in statistical physics. 
One way to bridge the scale between full atomistic models and more coarse-grained descriptions is to use Markov State 
models parameterized by the Eyring Kramers formulas. These formulas give the hopping rates between local minima of the 
potential energy function. They require to identify the local minima and saddle points of the potential energy function. 
This approach is for example used in materials science (kinetic Monte Carlo models).

In this talk, I will first present a recent result obtained in collaboration with D. Le Peutrec (Université d'Orléans) 
and B. Nectoux (Université Clermont Auvergne) about the mathematical foundations of this approach, by deriving these 
Eyring-Kramers exit rates starting from the overdamped Langevin dynamics [1]. I will then introduce a recent algorithm 
we proposed together with P. Parpas (Imperial College London) in order to locate saddle points [2]. I will explain why 
these two works both rely on concentration properties of the eigenvectors of Witten Laplacians, in the small temperature

[1] TL, D. Le Peutrec and B. Nectoux, Eyring-Kramers exit rates for the overdamped Langevin dynamics: the case with 
saddle points on the boundary,\\
[2] TL, P. Parpas, Using Witten Laplacians to locate index-1 saddle points, to appear in SIAM Journal on Scientific