Hugo Pourcelot personal webpage

Dipartimento di Matematica e Informatica 'Ulisse Dini'

Email adress : hugorobertbernard.pourcelot(AT)unifi.it

Since October 2023, I am postdoc at the Università degli studi di Firenze, working with Gabriele Vezzosi.

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

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.

Talks

Research 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

Working group talks

  • 2023, Università degli studi di Firenze, Workshop on groupoid structures on the filtered loop space and the Hodge degeneration, following Tasos Moulinos' paper
  • 2023, LAGA, Université Paris XIII, PhD student working group on factorization homology. Framings on manifolds and construction of factorization homology
  • 2023, Université Paris-Cité, Stratified Homotopy Hypothesis. \(\infty\)-categories of sheaves, Hypersheaves and constructibles sheaves on the category of conically smooth stratified spaces
  • 2021, LAGA, Université Paris XIII, Graph complexes. Loday-Quillen-Tsygan theorem (handwritten notes)
  • 2020, LAGA, Université Paris XIII, Grothendieck-Teichmüller group and applications. The operad of parenthesized braids and the group GT (handwritten notes)
  • 2020, LAGA, Université Paris XIII, Condensed mathematics. Condensed abelian groups
  • 2019, ENS Paris, Gaitsgory–Lurie’s proof of Weil’s conjecture. Constructible \(\ell\)-adic sheaves, Introduction to \(\mathbb{E}_\infty\)-algebras.
  • 2019, LAGA, Université Paris XIII, Mandell’s theorem. The Eilenberg--Moore spectral sequence (pdf notes)
  • 2019, IMAG, Montpellier, Multiple zeta values in deformation quantization. On the little disk operads

Popularization talks

  • 2022, PostGraduate forum, Lancaster University, Kontsevich’s theorem on deformation quantization
  • 2022, LAGA, Université Paris XIII, PhD students seminar, Le théorème de quantification par déformation de Kontsevich
  • 2020, LAGA, Université Paris XIII, PhD students seminar, Mathématiques des systèmes de vote (slides of the presentation)


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