Professor at Grenoble INP - Ensimag, member of Inria Grenoble Rhône-Alpes

Work address :

Inria Grenoble Rhône-Alpes, Tripop Team

ZIRST Montbonnot, 655 avenue de l'Europe

38334 Saint Ismier, France

Email : Guillaume.James_at_inria.fr

I am a member of the Tripop Team at Inria Grenoble Rhône-Alpes. The team was created on January 2018 as a follow-up of the Bipop Project-Team. Our team focuses on the analysis, simulation and control of nonsmooth dynamical systems and their applications. The latter include mechanical systems with impacts and friction, nonlinear electrical circuits, cyber-physical systems, and biological networks (spiking neurons, gene networks).

I am professor of applied mathematics at the Ensimag School of Informatics, Applied Mathematics and Telecom, which is part of Grenoble INP and Communauté Université Grenoble Alpes.

Research overview

My research is centered on nonlinear waves, with strong emphasis on spatially discrete systems and localized waves, such as solitary waves (traveling steadily) or breathers (involving oscillations). My main activity concerns the mathematical analysis of nonlinear waves (existence, qualitative properties) in smooth or nonsmooth models, and the derivation of amplitude equations that simplify their analysis and simulation. For this purpose I use techniques from bifurcation theory (in infinite dimensions) and multiscale analysis. I also work on computational aspects of nonlinear waves (Newton-type methods for time-periodic and traveling waves, time-integration schemes preserving dissipation). Applications include : impacts and vibrations in granular media and mechanical metamaterials, stick-slip at frictional interfaces, localized waves in biomolecules (vibrations in DNA, coupled mechanical-ionic waves along actin) and internal waves in stratified fluids.

Teaching

I give most of my lectures at Ensimag. I coordinate the common core course on numerical methods and the associated programming project (around 240 first year students) and I give a second year course on dynamical systems (these courses correspond to a Master 1 level).

I also teach undergraduate courses in the Classes Préparatoires at Grenoble INP (normed spaces and applications) and at Université Grenoble Alpes (introduction to applied mathematics, dynamical systems).

Some lecture notes are available here (in French).