Publications

Research Interests: homotopical algebra, operadic calculus and formality
My CV is available upon request.

Preprint

Kaledin classes and formality criteria, Arxiv 2404.17529 [46 pages].

Abstract: We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded algebras over operads or properads, possibly colored in groupoids. The present treatment generalizes the previous obstruction classes in two directions: outside characteristic zero and including a wider range of algebraic structures. This enables us to establish novel formality criteria, including formality descent with torsion coefficients, formality in families, intrinsic formality, and criteria in terms of chain-level lifts of homology automorphism.

Publication

A prop structure on partitions, avec Dana Hunter, Muriel Livernet, Christine Vespa et Inna Zakharevich, à paraître dans Women in Topology IV proceedings, Topology and its Applications, Arxiv 2402.12895 [17 pages].

Abstract: Motivated by its link with functor homology, we study the prop freely generated by the operadic suspension of the operad Com. We exhibit a particular family of generators, for which the composition and the symmetric group actions admit simple descriptions. We highlight associated subcategories of its Karoubi envelope which allows us to compute extensions groups between simple functors from free groups. We construct a particular prop structure on partitions whose composition corresponds to the Yoneda product of extensions between exterior power functors.

Survey

Lecture notes on weight structures and formality, with Geoffroy Horel, Higher Structure and Operadic Calculus, Advanced Courses in Mathematics - CRM Barcelona, Springer, 2024, Arxiv 2406.19142 [40 pages].

Patent

Method and system for detecting a living being or an object on a traffic lane, with Nicolas Chaintreuil, Thierry Creuzet et Sylvain Lespinats, Commissariat à l'énergie atomique et aux énergies alternatives, 2020, n° WO/2020/030877. [44 pages].