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, MongeAmpère 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 semidiscrete setting (i.e.
when transporting an absolutely continuous measure to a discrete one).
I am also investigating applications to inverse problems arising in nonimaging 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: smoothfractal 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
 StableProxies (ANR 20222026, PI: D. Coeurjolly)
 Raymapr: software to design optical components (innovation project,
supported by AMIES (6 months) and UGA through an IRGA Grant (12 months), 20232024, PI: B. Thibert)
 Hevea: HprincipE, Visualisation Et Applications
 MAGA: Monge Ampère et Géometrie Algorithmique (ANR 20162022, PI: Q. Mérigot)
 CoMeDiC: Convergent Metrics for Digital Calculus (ANR 20152021, PI: J.O. Lachaud)
PhD Students and Postdocs
 JeanBaptiste Follet (PhD, 2023...) Geometry of C1 isometric embeddings.
Coadvised with Vincent Borrelli
 Julien Prando (PhD, 2022...) Distributionally Robust Shape Optimization
Coadvised with Charles Dapogny (UGA IRGA Grant)
 Anatole Gallouet (PhD, 20192023) Inverse problems in nonimaging optics and generated jacobian equations
Coadvised with Quentin Mérigot
 JeanBaptiste Keck (Postdoc, January 2020  April 2021) Problèmes inverses en optique avec des sources de lumière étendues Coadvised with Quentin Mérigot (ANR MAGA Grant)
 Mélanie Theillière (PhD, 20162019) Effective Convex Integration Theory
Coadvised with Vincent Borrelli
 Jocelyn Meyron (PhD, 20152018) Transport optimal semidiscret et applications en optique anidolique
Coadvised with Quentin Mérigot
 Julien André (PhD, 20122015) Conception de réflecteurs pour des applications photométriques
Coadvised with Quentin Mérigot and Dominique Attali
 Roland Denis (Postdoc, December 2012 March 2014) Structure en fractale lisse des sphères de NashKuiper
Coadvised with Francis Lazarus within the Hevea Project (UJF Grant).
 Louis Cuel (PhD, 20112014) Discrete Geometric Inference
Coadvised with JacquesOlivier Lachaud
Main scientific and administrative responsabilities
Full CV in French, April 2022 (in the form of an activity report)