My research interest in short
My research focuses mainly on the study of Sobolev mappings with values into manifolds. I especially study questions related to the density of smooth maps among such mappings: strong and weak density problems, detecting topological singularities using analytical objects as the Jacobian, computing the relaxed energy, and so on. However, I am also interested in other questions linked to Sobolev spaces into manifolds, such as extension, lifting, or the study of harmonic maps.
Papers and preprints
- and , Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere, accepted for publication.
[PDF, 320K] arXiv:2403.12662 hal-04511102 - , An improved dense class in Sobolev spaces to manifolds, submitted for publication.
[PDF, 404K] arXiv:2402.17373 hal-04478523 - , A complete answer to the strong density problem in Sobolev spaces with values into compact manifolds, submitted for publication.
[PDF, 584K] arXiv:2305.12589 hal-04101953 - and , A decomposition for Borel measures , Real Anal. Exchange 48 (2023), no. 1, 83-99.
[PDF, 284K] arXiv:2010.15902 dial doi:10.14321/realanalexch.48.1.1629953964
Academic works
- My master thesis, written under the supervision of Petru Mironescu and Augusto Ponce.
This master thesis was the opportunity for me to discover Sobolev mappings with values into manifolds.
It is intended to be a summary of this fascinating domain, beginner-friendly, and with the minimum possible amount of prerequisites.
[PDF, 1.5M] - My bachelor thesis, written under the supervision of Augusto Ponce.
It is about measure theory, and more precisely about a generalization of a decomposition theorem due to Richard Delaware.
[PDF, 240K]
Other pedagogical documents
- In November 2024, I had the opportunity to give a 6h minicourse on Sobolev mappings to manifolds at ICMAT (Madrid, Spain).
In support of these lectures, I wrote a set of lecture notes, that might hopefully be useful to anyone looking for a soft introduction to this beautiful topic, accessible with a minimal amount of prerequisites, as well as a list of references.
They may remain quite sketchy, but I might improve them in the future (suggestions are welcome!).
See the timecode on the footer to know when they were last updated.
[PDF, 712K]
Invited talks
You will find here a list of the talks that I had the honor of giving, along with the pdf file containing the slides if I used some. (For historical accuracy reasons, the slides are not modified after their use. In particular, if you found mistakes on them, you will find all the evidence here!)
- November 2024, International Prague seminar on function spaces
- Sobolev mappings to manifolds: when geometric analysis interacts with function spaces
[PDF, 608K] - October 2024, CUNEF Universidad, Quantitative Methods Seminar
- Harmonic maps into the sphere: how bad can they be?
[PDF, 268K] - October 2024, Institut de Mathématiques de Toulon, Analysis and Applications Seminar
- Applications harmoniques à valeurs dans la sphère : à quel point peuvent-elles mal se comporter ?
[PDF, 268K] - May 2024, Institut de Mathématiques de Marseille, Applied Analysis Seminar
- The strong density problem in Sobolev spaces of maps with values into manifolds
[PDF, 596K] - January 2024, University of Warsaw, Insitute of Mathematics
- Strong density in Sobolev spaces to manifolds
[PDF, 528K] - November 2023, Institut de Mathématiques d'Orsay, Harmonic analysis seminar
- A complete answer to the strong density problem for Sobolev spaces with values into manifolds
[PDF, 548K] - September 2023, Institut de Mathématiques de Toulouse, Analysis Seminar
- A complete answer to the strong density problem for Sobolev spaces with values into manifolds
[PDF, 544K] - February 2023, Institut Camille Jordan (Université Lyon 1), Young analysts and modelers day
- A complete answer to the strong density problem for Sobolev spaces with values into manifolds
[PDF, 144K] - February 2023, Institut de Recherche en Mathématique et en Physique (UCLouvain), Nonlinear analysis seminar
- A complete answer to the strong density problem for Sobolev spaces with values into manifolds
[PDF, 232K]
Participation to conferences, schools, and so on
You will find here a list of scientific events to which I had the pleasure to participate. If I gave a talk or a poster, you will also find the pdf file here.
- August 2024, Bucharest
- The 16th French-Romanian Colloquium on Applied Mathematics
Talk: [PDF, 284K] - July 2024, Bonn
- Summer school Maximal Operators and Applications organized by the Hausdorff School of Mathematics
- June 2024, Będlewo
- Conference Geometric and Variational Analysis in memory of Jan Malý
Lightning talk: [PDF, 56K]; poster: [PDF, 188K] - November 2023, Clermont-Ferrand
- Journées EDP Auvergne-Rhône-Alpes
- July 2023, Chęciny
- Summer school Geometric Analysis and PDEs
Poster: [PDF, 600K] - June 2023, Caserta
- 45th symposium of the Real Analysis Exchange
Talk: [PDF, 296K] - March 2023, Bonn
- Spring school Recent trends in the mathematics of complex materials of the Hausdorff Institute of Mathematics
- December 2022, Nancy
- Meeting of the GDR-Calva