Philippe Malbos

Fields of interest

Algebraic rewriting: Higher-dimensional rewriting, (non)commutative Gröbner bases, Janet bases.
Homological algebra. Algebraic coherence. Homotopical conditions of finite convergence.
Plactic-like structures. Crystal structures.
Persistent homology. Topological Data Analysis.
History of mathematics: symbolic computation in the 20th century.

Publications

Repository of e-prints and bibliographic databases : ArXiv, Hal, MathSciNet, zbMATH GScholar.

Rewriting in internal monoids, in preparation.
Higher-dimensional cartesian normalization strategies, (with Samuel Mimram), in preparation.
String of columns rewriting and plactic-like data structures, (with Nohra Hage), in preparation.
Algebraic coherent confluence and higher-dimensional globular Kleene algebras, (with Cameron Calk, Eric Goubault, and Georg Struth), 2020, arXiv:2006.16129.
Algebraic polygraphs modulo and linear rewriting, (with Cyrille Chenavier and Benjamin Dupont), 2020, arXiv:2004.14361.
Coherence of monoids by insertions and Chinese syzygies, (with Nohra Hage), 2019, submitted, arXiv:1901.09879, hal-02015084.
Coherent confluence modulo relations and double groupoids, (with Benjamin Dupont), 2018, submitted, arXiv:1810.08184, hal-01898868.
Coherence of string rewriting systems by decreasingness, (with Clément Alleaume), submitted, 2017, arXiv:1612.09193, hal-01676936.
Maurice Janet’s algorithms on systems of linear partial differential equations, (with Kenji Iohara), Archive for History of Exact Sciences, to appear, 2020,
arXiv:1911.09703, hal-02375192.
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.
arXiv:1812.05062, hal-02015088.
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, Springer, 2020.
arXiv:1801.00053, hal-01673715.
Noncommutative linear rewriting: applications and generalizations, in Two algebraic byways from differential equations: Gröbner Bases and Quivers, Algorithms and Computation in Mathematics, vol. 28, Springer, 2020.
hal-01718880.
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.
arXiv:1406.0815, hal-01006220v3.
Polygraphs of finite derivation type, (with Yves Guiraud), Mathematical Structures in Computer Science, Vol. 28, Issue 2, pp. 155-201, 2018.
arXiv:1402.2587, hal-00932845.
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.
arXiv:1203.5358, hal-00682233.
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-Verlag, Vol. 8660, pp. 121-137, 2014.
hal-02084948.
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.
hal-00818253.
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-Verlag, 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, hal-02084961.

Talks and abstracts

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 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.

Archives

Announcements Journées LHC - Logique, homotopie, catégories, 2019, 16-17 octobre 2019, Lyon. Workshop Higher-dimensional Rewriting and Applications 2018, HDRA 2018, September 7, Oxford, United Kingdom. Workshop Higher-dimensional Rewriting and Applications 2017, HDRA 2017, September 8-9, Oxford, United Kingdom. 6th International Workshop on Confluence, IWC 2017, September 8th 2017, Oxford, United Kingdom. Conférence Catégories pour la théorie de l'homotopie et la réécriture, du 25 au 29 septembre 2017, CIRM, Marseille. Workshop Higher-dimensional Rewriting and Applications 2016, HDRA 2016, June 25-26, Porto, Portugal. Kobe-Lyon Summer School On Quivers : Computational Aspects and Geometric Applications, July 21-31, 2015, Kobe, Japan. Workshop Higher-dimensional Rewriting and Applications 2015, HDRA 2015, June 28-29, Warsaw, Poland. Conference Homotopy in Concurrency and Rewriting, June 9-11, 2015, Palaiseau. Workshop Algebras, Operads and Rewriting, September 30 – October 3, 2014, Saint-Étienne. Session thématique Mathematical Structures of Computation, 13 janvier - 14 février 2014, Lyon. Conférence Algebra and computation, 20 janvier - 24 janvier 2014, Lyon. École d'hiver Algebra and computation, 27 février - 2 mars 2012, CIRM, Marseille, dans le cadre de la session Logic and interactions 2012, CIRM, Marseille, 30 Janvier - 2 Mars 2012. Conférence Operads and Rewriting, 2-4 Novembre 2011, Lyon. Groupe de travail Invariants algébriques en informatique (2009-2010). Rencontre ANR INVAL, Lyon, 25-26 septembre 2008. Rencontre ANR INVAL, Strasbourg, 9 novembre 2006. Groupe de travail Frontières (2006). Rencontre Simplicial and Cubical Sets and Knowledge Evolution in Distributed Systems, 3-4 mai 2004, Paris.

Projects. Projet ANR Catégories, Homotopie et Réécriture. Projet Formalisation du calcul algebrique. Applied and Computational Algebraic Topology.