Fields of interest

Algebraic rewriting: higherdimensional and linear rewriting.

Higher algebra: (strict) ωcategories, polygraphs and computads, operads, properads, PROPS.

Categorification and formalisation of rewriting: algebraic coherence, Kleene algebras, singleset ωcategories.

Topological data analysis: persistent homology, topological process analysis in bioscience.

Further
Recent preprints and publications

Singleset cubical categories and their formalisation with a proof assistant, (with Tanguy Massacrier and Georg Struth), submitted, 2024, arXiv:2401.10553.
arXiv

Higher catoids, higher quantales and their correspondences, (with Cameron Calk, Damien Pous, and Georg Struth), submitted, 2023, arXiv:2307.09253.

Persistent homology of directed spaces, (with Cameron Calk and Eric Goubault), submitted, 2023, arXiv:2305.03357.

Persistent homology reveals strong phylogenetic signal in threedimensional protein structures, (with Léa Bou Dagher, Céline BrochierArmanet, and Dominique Madern), PNAS Nexus, to appear, 2024.

Polygraphs: from rewriting to higher categories, (with Dimitri Ara, Albert Burroni, Yves Guiraud, François Métayer, and Samuel Mimram), London Mathematical Society Lecture Note Series, to appear, 2024.
arXiv, HAL

Shuffle polygraphic resolutions for operads,
(with Isaac Ren), Journal of the London Mathematical Society, Vol. 107, Issue 1, pp. 61122, 2023.
DOI, arXiv, HAL
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