Let us give a few examples. In materials science, it is now possible to simulate the dynamics of defects in a crystallin lattice, which is a fundamental mechanism to understand the ageing of nuclear reactor. In biological sciences, the simulation of the interaction between a protein and a ligand is crucial to predict the influence of the ligand on the behavior of the protein, with applications to drug design for example. The computer can thus be used as a “numerical microscope” in order to access data that would be very difficult and costly to obtain experimentally.

In order to make these simulations efficient and precise, mathematics have a crucial role to play. Indeed, specific algorithms have to be used in order to bridge the time and space scales between the atomistic level and the macroscopic level. The objective of the MSMath ERC project is thus to develop and study efficient algorithms to simulate high-dimensional systems over very long times. These developments are done in collaboration with physicists, chemists and biologists who are using these numerical methods in an academic or industrial context.

In particular, we are developping mathematical tools at the interface between the analysis of partial differential equations and stochastic analysis in order to characterize and to quantify the metastability of stochastic processes. Metastability is a fundamental concept to understand the timescale separation between the microscopic model and the macroscopic world. Many algorithms which aim at bridging the timescales are built using this timescale separation.