Philippe Malbos

Fields of interest

Algebraic rewriting: higher-dimensional rewriting, (non)commutative Gröbner bases, Janet bases.
Strict ω-categories, polygraphs and computads, operads, properads, PROPS.
Modal Kleene algebras, algebraic coherence, abstract rewriting systems.
Homological algebra, homotopical conditions of finite convergence.
Persistent homology. Topological Data Analysis.
Topological Process Analysis in computer science and biology.
Plactic-like structures. Crystal structures.
History of mathematics: symbolic computation in the 20th century.

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.

Repository of e-prints and bibliographic databases

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

Preprints submitted or accepted and work in progress

Rewriting in internal monoids, in preparation.
Higher-dimensional cartesian normalization strategies, (with Samuel Mimram), in preparation.
String of columns rewriting and confluence of the jeu de taquin, (with Nohra Hage), 2022, arXiv:2012.15649, hal-03161577.

Publications

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.

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.
DOI, HAL.

Presentation for general audience

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

Abstracts, talks and unpublished texts

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.
Musée des confluences , January 2015.
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.