Philippe Malbos

Research
Teaching

Professor at
Institut Camille Jordan
Université Claude Bernard Lyon 1

Contact and location

Fields of interest

• Algebraic rewriting: higher-dimensional and linear rewriting.
• Higher algebra: (strict) ω-categories, polygraphs and computads, operads, properads, PROPS.
• Categorification and formalisation of rewriting: algebraic coherence, Kleene algebras, single-set ω-categories.
• Topological data analysis: persistent homology, topological process analysis in bioscience.
• Further

Recent preprints and publications

• Higher catoids, higher quantales and their correspondences, (with Cameron Calk, Damien Pous, and Georg Struth), submitted, 2023, arXiv:2307.09253.
• Single-set cubical categories and their formalisation with a proof assistant, (with Tanguy Massacrier and Georg Struth), Journal of Automated Reasoning, Vol. 68, No. 20, 2024.
  DOI, HAL, Extended version on arXiv
• Persistent homology of partially ordered spaces, (with Cameron Calk and Eric Goubault), Journal of Applied and Computational Topology, to appear, 2024.
  DOI, HAL, arXiv
• Persistent homology reveals strong phylogenetic signal in three-dimensional protein structures, (with Léa Bou Dagher, Céline Brochier-Armanet, and Dominique Madern), PNAS Nexus, pgae 158, 2024.
  DOI, HAL, data
• 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

Preprints and work in progress

Publications

Announcements

• Double Licence Mathématiques - Sciences de la Vie : nouvelle formation de premier cycle à Lyon à l'interface des mathématiques et des sciences de la vie conduisant à un diplôme dans chaque discipline.


• Higher Algebra and Formalised Mathematics : new thematic program
  in the Advanced Mathematics second year program 2024–2025, poster.







• Working group:
  Persistent homology and Molecular biology

Lectures notes

• Lectures on Algebraic Rewriting, partial notes (chapters 1 to 7), in progress.

Editorial

• Editor of Mathematical Structures in Computer Science.

• Book: Two algebraic byways from differential equations: Gröbner Bases and Quivers, edited by K. Iohara, P. Malbos, M.-H. Saito, N. Takayama, series Algorithms and Computations in Mathematics, volume 28, Springer, 2020, hal-02084961.

Member of

• Société mathématique de France, Société informatique de France, GDR théorie de l’homotopie et applications, GDR Informatique Mathématique (GdR IM), Groupe de travail Logique, Homotopie, Catégories (LHC) du GdR IM.