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Hi! I'm Sacha.
From September 1st 2024, I am a maître de conférences (équivalent Associate Professor) at Université de Strasbourg, in France. I am part of the Algèbre, Représentation, Topologie team of the IRMA research unit.
Before that, I was a postdoctoral scholar at the University of Calgary, in Canada, with Kristine Bauer, and at the University of Ottawa, in Canada, with Rick Blute, Simon Henry, and Philip Scott.
My research interests are in algebraic topology, homotopy theory and category theory. I am especially interested in operads and their divided powers. I also did some work on unstable modules and algebras over the Steenrod algebra. More recently, I have worked with JSPL on a notion of differential and tangent categories. I have a project with Tim Van der Linden aiming to study the category of algebras over a reduced operad as a semi-abelian category, and investigating links between semi-abelian categories and differential and tangent categories. I also have a somewhat more ambitious project to define a rigorous framework for divided powers in general categories, with applications in topology, functor calculus, and possible extensions to the ∞-category and ∞-operad viewpoint.
Publications
Publications
Not-yet-published :
Not-yet-published :
Tangent structures for divided power algebras, 2025.
arxiv preprint: https://arxiv.org/abs/2508.16302
Published articles :
Published articles :
Quillen (co)homology of divided power algebras over an operad, with Ioannis Dokas and Martin Frankland. 2024.
Accepted for publication in Annales de l'Institut Fourier, 2025.
arxiv preprint: https://arxiv.org/abs/2403.18049
The Rosický tangent categories of algebras over an operad, with Marcello Lanfranchi and Jean-Simon Pacaud Lemay.
Higher Structures, Volume 8, 2024 Number 2, pp. 332–385.
https://higher-structures.math.cas.cz/api/files/issues/Vol8Iss2/IkoLanLem
Unstable algebras over an operad II. Homology, Homotopy, and Applications, Volume 26, 2024 Number 1, pp. 37-67
arXiv preprint: https://arxiv.org/abs/2011.13002
Cartesian differential comonads and new models of cartesian differential categories, with Jean-Simon Pacaud Lemay. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 64-2, 2023, pp 198–239.
arXiv preprint: https://arxiv.org/abs/2108.04304
Divided power algebras and distributive laws. Journal of Pure and Applied Algebra, Volume227, Issue 8, August 2023.
arXiv preprint: https://arxiv.org/abs/2104.11736
Unstable algebras over an operad. Homology, Homotopy, and Applications, Volume 23, 2021, Number 1, pp. 119–141.
https://www.intlpress.com/site/pub/pages/journals/items/hha/content/vols/0023/0001/a008/index.php
Divided power algebras over an operad. Glasgow Mathematical Journal, Volume 62, Issue 3, September 2020, pp. 477 - 517.
arXiv preprint: https://arxiv.org/abs/1712.03694
Academic career
Academic career
2023 — 2024: Postdoctoral fellow with Rick Blute, Simon Henry, and Philip Scott. University of Ottawa, Ottawa ON, Canada
2020 — 2022 : Postdoctoral scholar with Kristine Bauer, University of Calgary, Calgary AB, Canada
2019 — 2020 : ATER (temporary teaching and research assistant), Université de Paris, Paris, France
2016 — 2019 : PhD, Université de Paris, Paris, France :
Advisor : Muriel Livernet
Thesis : Level algebras and applications to algebraic topology
2014 — 2016 : Master de mathématiques fondamentales, Université Pierre et Marie Curie, Paris, France :
Advisor : Muriel Livernet
Master thesis : Homotopie des algèbres simpliciales sur une opérade
2010 — 2014 : Licence de Mathématiques, Université Pierre et Marie Curie, Paris, France
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