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Paul Laubie
paul dot laubie at univ-lorraine dot fr

I am currently a post-doc researcher at Institut Elie Cartan de Lorraine, UMR 7502 de l'Université de Lorraine under the supervision of Yvain Bruned .

I'm very interested in combinatorics, algebraic operads and homotopy theory and more precisely relationship between those.

I'm currently in the team Probabilités et Statistique . This may seem incongruous given my research interest, however, Algebraic Operads have proven useful in Regularity Structures which are used to solve SPDEs.

Academic path

2024-now Post-doc at the Institut Elie Cartan de Lorraine, UMR 7502 de l'Université de Lorraine under the supervision of Yvain Bruned .
2021-2024 PhD at the Institut de Recherche Mathématique Avancée, UMR 7501 de l'Université de Strasbourg in the team ART: Algèbre, représentations, topologie under the supervision of Vladimir Dotsenko .
2017-2021 Magister of Mathematics at the ÉNS de Rennes.
2018-2021 Master pathway in Fundamental Mathematics at the Université de Rennes 1.
2018-2020 Master pathway Préparation à l'agrégation externe at the Université de Rennes 1.

Research

Preprints

2026 with Yvain Bruned, and Aurélien Minguella, On the equivalence between the Polchinski flow and the Connes-Kreimer approaches to perturbative renormalisation.
2026 Braces on the cohomology of noncrossing 2-partitions.
2026 with Yvain Bruned, Yingtong Hou, and Zhicheng Zhu, Banach fixed point and flow approach for rough analysis.
2025 Homological freeness criterion for operadic modules and application to Cohen-Macalayness of posets.
2025 On Hilbert series of Koszul operads and a classification result for set-operads. Link to the additionnal file here.
2025 with Yvain Bruned, Elementary differentials from multi-indices to rooted trees.

Publications

2025 Hypertrees and embedding of the FMan operad, published in IMRN, ArXiv version here.
2025 with Vladimir Dotsenko, Volume preservation of Butcher series methods from the operad viewpoint, published in IMRN, ArXiv version here
2026 Combinatorics of pre-Lie products sharing a Lie bracket, to be published in Algebraic Combinatorics.

PhD thesis

Feel free to send me an email if you find any typo. I know there is still a lot of them.

2024 Combinatorics, Homotopy, and Embedding of operads.

Master thesis

2021 The Losev-Manin shuffle algebra.

Teaching

2026-2027 I am teaching Système Logique et Codage Numérique (encoding of information in computers) at the Université de Lorraine.

2026-2027 I am teaching the exercise sessions of Mathématiques Discrètes (discrete Mathematics) at the Université de Lorraine.

2021-2024 I was teaching Algèbre S2 (linear algebra) at the Université de Strasbourg.

Miscellaneous

PhD student workshop I have followed at the Université de Strasbourg:

Workshop on characteristic classes.
Workshop on algebraic stacks.

PhD student workshop I have organized at the Université de Strasbourg:

Workshop on condensed math.
Workshop on infinity-categories.