Hugo Pourcelot personal webpage

Laboratoire Géométrie, Analyse et Applications (LAGA)
Algebraic topology group
Université Paris XIII (aka Université Sorbonne Paris Nord)

Email adress : pourcelot@math.univ-paris13.fr

I am currently ATER (~ temporary researcher and lecturer) in mathematics at the university Paris 13 until August 2023.

I defended my PhD thesis untitled "The brane action for coherent ∞-operads" on the 13th of December 2022 at the university Paris XIII, under the supervision of Grégory Ginot.

Research

Main research interests : algebraic topology, homotopy theory, ∞-operads, higher category theory, derived geometry, topological quantum field theories

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.

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