Research
Main research interests : derived algebraic geometry, algebraic topology, homotopy theory, ∞-operads
Prepublications
- Brane actions for coherent ∞-operads, (arXiv:2302.12206, HAL), February 2023
Abstract. We prove that Mann-Robalo's construction of the brane action extends to general coherent ∞-operads, with possibly multiple colors and non-contractible spaces of unary operations. This requires to establish two results regarding spaces of extensions that were left unproven in the aforementioned construction. First, we show that Lurie's and Mann-Robalo's models for such spaces are equivalent. Second, we prove that the space of extensions in the sense of Lurie is not in general equivalent to the homotopy fiber of the associated forgetful morphism, but rather to its homotopy quotient by the ∞-groupoid of unary operations, correcting an oversight in existing literature. As an application, we obtain that the ∞-operads of B-framed little disks are coherent and therefore yield new operations on spaces of branes of perfect derived stacks.
PhD Thesis
Manuscript of my PhD thesis: The brane action for coherent ∞-operads
Video of the defence: PhD defence
This program has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 754362.
Contributed talks
- December 2023, EPFL
- October 2023, Firenze, String topology, operads and the brane action
- July 2023, EPFL, Young Topologists Meeting: The brane action and string topology (slides of the presentation)
- January 2023, Toulouse, L’action de membranes et ses applications géométriques
- October 2022, Nantes, Autour de l’action de membranes et ses applications géométriques
- October 2021, Strasbourg, Annual congress of the GDR "Topologie et applications", On the brane action
- December 2018, Angers, Starting conference of the ANR CatAG
Teaching
2022-2023
- M1 - Arithmétique
- L3 - Tutorat
- L2 - Algèbre 3 (Double Licence)
- L2 - Analyse 3 - Séries et Intégrales généralisées
- L1 - Programmation 2 : Structures de données
- L3 - Analyse 6 - analyse complexe
2021-2022
- M1 - Arithmétique
- L2 - Algèbre 3 (Double Licence)
- L2 - Analyse 3 - Séries et Intégrales généralisées
- L3 - Algèbre 6
- Parcours aménagé - Outils mathématiques
2020-2021
- L2 - Analyse 3 - Séries et Intégrales généralisées
- L2 - Algèbre 3
2019-2020
- L2 - Analyse 3 - Séries et Intégrales généralisées
- L2 - Algèbre 3
2018-2019
- M2 - Introduction à la théorie de l'homotopie
- L1 - Algèbre linéaire et algorithmique