Philippe Malbos

Fields of interest

Topological data analysis in evolutionary biology : persistent homology, spectral geometry, protein 3D structures, evolution, life history traits.
Categorification and formalisation of rewriting: algebraic coherence, Kleene algebras, single-set ω-categories.
Algebraic rewriting: higher-dimensional, modulo and linear rewriting, (non)commutative Gröbner bases, Janet bases.
Higher algebra: (strict) ω-categories, polygraphs and computads, operads, properads, PROPS.
Homological and homotopical algebra in rewriting theory.
Persistent homology. Topological Data Analysis. Topological Process Analysis in computer science.
Plactic-like and crystal structures.
History of mathematics: symbolic computation in the 20th century.

Fields of interest (Mathematics Subject Classification 2020)

Preprints submitted or accepted and work in progress

Abstract rewriting cubes and normalisation strategies, (with Tanguy Massacrier and Georg Struth), in progress.
Coherent confluence of operad algebras, (with Yoann Dabrowski and Isaac Ren), in progress.
Extraction of thermoadaptation fingerprints from 3D protein structures using machine learning and persistent homology, (with Léa Bou Dagher and Céline Brochier-Armanet), in progress.
Polygraphic resolutions for operated algebras, (with Zuan Liu), submitted, 2025, arXiv:2502.16304.

Repository of e-prints and bibliographic databases

ORCID, HAL, arXiv, zbMATH, MathSciNet, GScholar, ResearchGate.

Publications

Higher catoids, higher quantales and their correspondences, (with Cameron Calk, Damien Pous, and Georg Struth), Applied Categorical Structures, Vol. 33, No. 25, 2025.
DOI, arXiv
Faithful interpretation of protein structures through weighted persistent homology improves evolutionary distance estimation, (with Léa Bou Dagher, Céline Brochier-Armanet, and Dominique Madern), Molecular Biology and Evolution, Vol. 42, Issue 2, msae271, 2025.
DOI, HAL
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, Vol. 8, pp. 2247-2284, 2024.
DOI, arXiv, HAL
Persistent homology reveals strong phylogenetic signal in three-dimensional protein structures, (with Léa Bou Dagher, Céline Brochier-Armanet, and Dominique Madern), PNAS Nexus, Vol. 4, Issue 4, pgae158, 2024.
DOI, HAL, data
Shuffle polygraphic resolutions for operads, (with Isaac Ren), Journal of the London Mathematical Society, Vol. 107, Issue 1, pp. 61-122, 2023.
DOI, arXiv, HAL
Algebraic coherent confluence and higher globular Kleene algebras, (with Cameron Calk, Eric Goubault, and Georg Struth), Logical Methods in Computer Science, Vol. 18, Issue 4, pp. 9:1–9:43, 2022.
DOI, arXiv, HAL
Coherent confluence modulo relations and double groupoids, (with Benjamin Dupont), Journal of Pure and Applied Algebra, Vol. 226, Issue 10, 107037, 2022.
DOI, arXiv, HAL
Confluence of algebraic rewriting systems, (with Cyrille Chenavier and Benjamin Dupont), Mathematical Structures in Computer Science, Vol. 32, Issue 7, 870-897, 2022
DOI, arXiv, HAL
Chinese syzygies by insertions, (with Nohra Hage), Semigroup Forum, Vol. 104, pp. 88-108, 2022.
DOI, arXiv, HAL
Abstract strategies and coherence, (with Cameron Calk and Eric Goubault), 19th International Conference on Relational and Algebraic Methods in Computer Science (RAMICS 2021), Lecture Notes in Computer Science, Springer, Vol. 13027, pp. 108-125, 2021.
DOI, HAL
Completion in operads via essential syzygies, (with Isaac Ren), Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation (ISSAC 2021), Association for Computing Machinery, pp. 305-312, 2021.
DOI, HAL
Maurice Janet’s algorithms on systems of linear partial differential equations, (with Kenji Iohara), Archive for History of Exact Sciences, Vol. 75, pp. 43-81, 2021.
DOI, arXiv, HAL
Time-reversal homotopical properties of concurrent systems, (with Cameron Calk and Eric Goubault), Homology, Homotopy and Applications, Vol. 22, No. 2, pp. 31-57, 2020.
DOI, arXiv, HAL
From analytical mechanical problems to rewriting theory through M. Janet, (with Kenji Iohara), in Two algebraic byways from differential equations: Gröbner Bases and Quivers, Algorithms and Computation in Mathematics, Vol. 28, pp. 3-74, Springer, 2020.
DOI, arXiv, HAL
Noncommutative linear rewriting: applications and generalizations, in Two algebraic byways from differential equations: Gröbner Bases and Quivers, Algorithms and Computation in Mathematics, Vol. 28, pp. 115-183, Springer, 2020.
DOI, HAL
Convergent presentations and polygraphic resolutions of associative algebras, (with Yves Guiraud and Eric Hoffbeck), Mathematische Zeitschrift, Vol. 293, Issue 1–2, pp. 113-179, 2019.
DOI, arXiv, HAL
Polygraphs of finite derivation type, (with Yves Guiraud), Mathematical Structures in Computer Science, Vol. 28, Issue 2, pp. 155-201, 2018.
DOI, arXiv, HAL
Knuth's coherent presentations of plactic monoids of type A, (with Nohra Hage), Algebras and Representation Theory, Vol. 20, Issue 5, pp. 1259-1288, 2017.
hal-01359677, long version: arXiv:1609.01460.
Homological Computations for Term Rewriting Systems, (with Samuel Mimram), 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016), LIPIcs. Leibniz Int. Proc. Inform., Vol. 52, pp. 27:1-27:17, 2016.
hal-01678175.
Coherent presentations of Artin monoids, (with Stéphane Gaussent and Yves Guiraud), Compositio Mathematica, Vol. 151, No. 5, pp. 957-998, 2015.
DOI, arXiv, HAL.
Eigenvalue method with symmetry and vibration analysis of cyclic structure, (with Aurélien Grolet and Fabrice Thouverez), 16th International Workshop on Computer Algebra in Scientific Computing (CASC 2014), Lecture Notes in Computer Science, Springer, Vol. 8660, pp. 121-137, 2014.
DOI, HAL.
A Homotopical Completion Procedure with Applications to Coherence of Monoids, (with Yves Guiraud and Samuel Mimram), 24th International Conference on Rewriting Techniques and Applications (RTA 2013), LIPIcs. Leibniz Int. Proc. Inform., Vol. 21, pp. 223-238, 2013.
DOI, HAL.
Identities among relations for higher-dimensional rewriting systems, (with Yves Guiraud) Séminaires et Congrès, Société Mathématique de France, Vol. 26, pp. 145-161, 2013.
arXiv:0910.4538, hal-00426228.
Higher-dimensional normalisation strategies for acyclicity, (with Yves Guiraud), Advances in Mathematics, Vol. 231, No. 3–4, pp. 2294–2351, 2012.
arXiv:1011.0558, hal-00531242.
Coherence in monoidal track categories, (with Yves Guiraud), Mathematical Structures in Computer Science, Vol. 22, Issue 6, pp. 931-969, 2012.
arXiv:1004.1055, hal-00470795.
Higher-dimensional categories with finite derivation type, (with Yves Guiraud), Theory and Applications of Categories, Vol. 22, No. 18, pp. 420-478, 2009.
arXiv:0810.1442, hal-00326974.
Rewriting Systems and Hochschild-Mitchell Homology, Electronic Notes in Theoretical Computer Science, Vol. 81, Elsevier, 2003.
Modelling through human-computer interactions and mathematical discourse, (with G. M. da Nóbrega and J. Sallantin), Applied Logic Series, Vol. 25, pp. 293-311, 2002.
The Blob: A Basic Topological Concept for "Hardware-free" Distributed Computation, (with Frédéric Gruau) Lecture Notes in Computer Science, Springer, Vol. 2509, pp. 151-163, 2002.

Books

Polygraphs: from rewriting to higher categories, (with Dimitri Ara, Albert Burroni, Yves Guiraud, François Métayer, and Samuel Mimram), London Mathematical Society Lecture Note Series 495, Cambridge University Press, 2025.
arXiv, HAL

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.
DOI, HAL.

Editorial

Editor of Mathematical Structures in Computer Science.

Presentations for general audience

Raconte-moi... la persistance topologique, La Gazette des mathématiciens, Société Mathématiques de France, Vol. 169, pp. 44-50, 2021.
HAL
Musée des confluences , January 2015.

Abstracts, talks and unpublished texts

String of columns rewriting and confluence of the jeu de taquin, (with Nohra Hage), 2022, arXiv:2012.15649, hal-03161577.
Abstract abstract coherence and acyclicity, Geometric and Topological Methods in Computer Science - GETCO 2023 - Aalborg, July 2023.
Resolutions and abstract abstract coherence, Journées François Métayer, Paris, Juin 2023.
Completion of operadic rewriting systems by Gaussian elimination, (with Benjamin Dupont and Isaac Ren), International Workshop on Confluence (IWC 2021), July 2021.
Algebraic critical pair lemma, (with Cyrille Chenavier and Benjamin Dupont), International Workshop on Confluence (IWC 2020), June 2020.
Squier’s theory for monoids and algebras (slides in complement of the blackboard lecture), Categories in Homotopy Theory and Rewriting, CIRM, September 2017.
Coherence of string rewriting systems by decreasingness, (with Clément Alleaume), 2017, arXiv:1612.09193, hal-01676936.
Coherence of quasi-terminating decreasing 2-polygraphs, International Workshop on Confluence (IWC 2016), September 2016.
Confluence of linear rewriting and homology of algebras , International Workshop on Confluence (IWC 2014), July 2014.
Coherent presentations of Artin groups, October 2013.
A Homotopical Completion Procedure, Rewriting Techniques and Applications (RTA 2013), June 2013.
Algebraic confluences
- Part I. Homology and rewriting,
- Part II. Two-dimensional homotopy and rewriting,
Identities among relations for polygraphic rewriting.

Fields interest (Mathematics Subject Classification 2020)

Fields of primary interest (Mathematics Subject Classification 2020): 18N30, 68Q42, 18N10, 68Q70, 20M05, 18M85.
Secondary interest: 01A60, 03D05, 05E10, 13P10, 16D10, 16E05, 16S37, 16Z05, 18B40, 18C10, 18C50, 18D40, 18F75, 18G10, 18G15, 18G20, 18M05, 18M30, 20F36, 55U99, 57M05, 68Q80, 68Q85, 68R15, 68W15.

Philippe Malbos

Fields of interest

Preprints and work in progress

Publications

Fields of interest

Preprints submitted or accepted and work in progress

Repository of e-prints and bibliographic databases

Publications

Books

Editorial

Presentations for general audience

Abstracts, talks and unpublished texts

Fields interest (Mathematics Subject Classification 2020)

Archives