Professor of Applied Mathematics

Université Grenoble Alpes
Laboratoire Jean Kuntzmann
PDE Team




FirstName.LastName(adapted sign)univ-grenoble-alpes.fr
Snail Mail
Laboratoire LJK - Bâtiment IMAG
Université Grenoble Alpes
150 Place du Torrent
38400 Saint Martin d'Hères

Accès
Bureau 161 - bâtiment IMAG - Plan

Phone +33 4 57 42 17 84

Research interests

I am mostly interested in the development of effective calculations in problems having a geometric flavor, which could be refered as applied geometry or numerical geometry. In particular, I have been working in the field of geometric inference and on different nonlinear geometric problems, having connections with various domains such as optimal transport, Monge-Ampère equations, inverse problems in optics, computational geometry or convex integration theory. Below are some of my favorite fields I have contributed to.

Numerical optimal transport / Inverse problems in optics.
I am working on the numerical aspect of optimal transport, in particular in the semi-discrete setting (i.e. when transporting an absolutely continuous measure to a discrete one). I am also investigating applications to inverse problems arising in non-imaging optics.

Figure: Parallel light refracted by a lens that concentrates the light into the "hikari" character.
Convex Integration theory / Smooth fractals.
I am working with the Hevea Project on the realization of Nash's isometric embeddings based on the Convex Integration Theory developped by Gromov in the 70s. I am particularly interested in the simplification of this theory in order to make it more effective and to numerically solve some nonlinear partial differential equations.
Click here for an application of the flat torus.

Figure: smooth-fractal structure observed on a reduced sphere.
Geometric inference.
The aim of geometric inference is to get robust estimations of the topological and geometric properties of a geometric object from an approximation, such as a finite point set. I have in particular been working on the stability of the (Federer) curvature measures, the regularity of the distance functions to compact sets, Voronoi Covariance Measures using distances to measures.

Figure: Example of a finite point set from which one wants to infer geometric properties of the underlying object.

More details on my publications web page.

Current (and recent) projects

PhD Students and Postdocs

Main scientific and administrative responsabilities


Full CV in French, April 2022 (in the form of an activity report)