摘要：There are classical situations where preserving numerically specific geometric structures reveals essential for an accurate time integration of differential equations (for instance the symplecticity of the flow for Hamiltonian systems), and this is the essence of geometric numerical integration.

In this talk, we highlight the role that some geometric integration tools (in particular modified differential equations and processing techniques), that were originally introduced in the deterministic setting, play in the design of new accurate integrators to sample the invariant distribution of ergodic systems of stochastic ordinary and partial differential equations.

This talk is based on joint works with Assyr Abdulle (EPF Lausanne), Charles-Edouard Bréhier (Univ. Lyon) and Kostas Zygalakis (Univ. Edinburgh).

Professor Gilles Vilmart received his Ph.D. in Mathematics at University of Rennes 1 (INRIA Rennes) and University of Geneva (double doctorate program), and then worked as a post-doc at EPFL (2009-2011) and agrégé-préparateur at ENS Rennes (2011-2013). He is now a senior research associate at University of Geneva, Section of Mathematics. His research is on numerical analysis of differential equations (ODEs and PDEs with emphasis on multiscale and stochastic problems).