in French (in the form of an activity report)
Recent and upcoming events
- July 4 2022: Congrats to Jean-Baptiste Keck, who received the i-PhD prize for his contribution to the innovation project Anidolix.
- July 18-22 2022: Talk at the AMS-SMF-EMS conference in Grenoble, in the Special Session on Differential Geometry in the Tradition of Élie Cartan. I will speak about Generated Jacobian equations.
- May 15-20 2022 : I gave a 8 hours course at the Universita di Verona on Optimal transport: discretization and algorithms.
- May 13 2022 : Seminar at the Virtual Maxwell Analysis seminar, University of Edinburgh and Heriot-Watt University on generated jacobian equations arising in non-imaging optics.
- April 14 2022: I participated to a roundtable at the Université de Franche Comté after
the diffusion of the documentary "Ils ont eu raison du tore". This documentary is about our Hevea project and has been realized by Dominique and Geoffrey Garing.
- April 6-7 2022 : Talk at the Journées ANR Shapo, in Autrans on the numerical resolution of Generated Jacobian equations.
- Febr 2-4 2022 : I coorganized with Thomas Gallouet the last meeting of the ANR MAGA.
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.
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 2022-2026, PI: D. Coeurjolly)
- Anidolix: software to design optical components (PI: B. Thibert)
- Hevea: H-principE, Visualisation Et Applications
- MAGA: Monge Ampère et Géometrie Algorithmique (ANR 2016-2022, PI: Q. Mérigot)
- CoMeDiC: Convergent Metrics for Digital Calculus (ANR 2015-2021, PI: J.-O. Lachaud)
PhD Students and Postdocs
- Julien Prando (PhD, 2022-...) Distributionally Robust Shape Optimization
Co-advised with Charles Dapogny (UGA IRGA Grant)
- Anatole Gallouet (PhD, 2019-...) Inverse problems in nonimaging optics and generated jacobian equations
Co-advised with Quentin Mérigot
- Jean-Baptiste Keck (Postdoc, January 2020 - April 2021) Problèmes inverses en optique avec des sources de lumière étendues Co-advised with Quentin Mérigot (ANR MAGA Grant)
- Mélanie Theillière (PhD, 2016-2019) Effective Convex Integration Theory
Co-advised with Vincent Borrelli
- Jocelyn Meyron (PhD, 2015-2018) Transport optimal semi-discret et applications en optique anidolique
Co-advised with Quentin Mérigot
- Julien André (PhD, 2012-2015) Conception de réflecteurs pour des applications photométriques
Co-advised with Quentin Mérigot and Dominique Attali
- Roland Denis (Postdoc, December 2012- March 2014) Structure en fractale lisse des sphères de Nash-Kuiper
Co-advised with Francis Lazarus within the Hevea Project (UJF Grant).
- Louis Cuel (PhD, 2011-2014) Discrete Geometric Inference
Co-advised with Jacques-Olivier Lachaud
Laboratoire LJK - Bâtiment IMAG
Université Grenoble Alpes
700 Avenue Centrale
Bureau 161 - 1er étage - bâtiment IMAG
+33 4 57 42 17 84
(adapted sign) univ-grenoble-alpes.fr