Joost Vercruysse

Coordinates

Joost Vercruysse
Université Libre de Bruxelles
Département de Mathématique
Bureau 2.O.8.104 
Campus de la Plaine CP216
Boulevard du Triomphe
B-1050 Bruxelles - Belgium
Email: jvercruy - at - ulb.ac.be
Phone: +32-2-650.60.32






Research 

Main research interests are Algebra and Category theory.
More specifically, research topics include Hopf algebras and Hopf algebroids, Corings and Coalgebras, Hopf-Galois theory and Galois descent, non-commutative geometry and quantum groups.

Team

  • PhD students
    Florence Sterck | FRIA fellow | co-supervision with Marino Gran (UCL) | started in October 2017
    William Hautekiet | teaching assistant at ULB | started in October 2019
    Paul Grosskopf | FRIA fellow | started in October 2020
  • Postdocs
    Paolo Saracco | Chargé de recherche at FRNS | at ULB since May 2018
  • Former PhD students
    Isar Goyvaerts | teaching assistant VUB | co-supervision with Stef Caenepeel (VUB) | PhD defended August 2013 | thesis title : Techniques from monoidal category theory applied to generalized Lie algebras and various types of dualities
    Gabriel Kadjo | FRIA fellow | co-supervision with Marino Gran (UCL) | PhD defended September 2016 | thesis title : Semi-abelian aspects of cocommutative Hopf algebras
    Jiawei Hu | CSC grant | joint PhD between East China Normal University (local supervisor Sheng-Li Tan) and ULB | PhD defended July 2018 | thesis title: Partial actions in algebraic geometry
    Timmy Fieremans | teaching assistant VUB | co-supervision with Stef Caenepeel (VUB) | PhD defended September 2019 | thesis title: Hopf and Frobenius V-categories
    Hoan-Phung Bui | teaching assistant ULB | co-supervision with Gabor Wiese (Université de Luxembourg) | PhD defended September 2020 | thesis title : Correspondence theorems in Hopf-Galois theory for separable field extensions
  • Former Postdocs
    Mitchell Buckley | post-doctoral researcher on ARC project October 2015 - September 2016 | ULB individual fellowship December 2016 - May 2018
    Dimitri Chikhladze | post-doctoral researcher on ARC project | May 2016 - September 2016
    Christina Vasilakopoulou | post-doctoral researcher on ARC project | October 2016 - September 2017
    Jonathan Grant | post-doctoral researcher on ARC project | October 2016 - September 2017
    Réamonn O’Buachalla | post-doctoral researcher on MIS project | June 2018 - May 2020
    Alessandro Iraci | post-doctoral researcher my MIS project | November 2019 - March 2020
  • Long term visitors
    Eliezer Batista | Universidade Federal de Santa Catarina, Florianopolis, Brazil | January 2013 - January 2014
    Ana Cristina Correa Munaretto | Universidade de Paraná, Brasil | February 2014 - July 2014
    Matheus Teixeira | Universidade Federal de Santa Catarina, Florianopolis, Brazil | August 2017 - March 2018

Publications

  • As this website is determined to become outdated, more updated versions of the publication list, as well as free pdf-preprint versions of all papers can be found on arXivGoogle Scholar, Researchgate and DI-fusion.
  • Preprints
    P. Saracco and J. Vercruysse, Geometric partial comodules over flat coalgebras in Abelian categories are globalizable, arXiv:2107.07299
    P. Saracco and J. Vercruysse, On the globalization of geometric partial (co)modules in the categories of topological spaces and algebras, arXiv:2107.06574 
    A. Agore, A. Gordienko and J. Vercruysse, V-universal Hopf algebras (co)acting on Ω-algebras, arXiv:2005.12954
    M. D'Adderio, W. Hautekiet, P. Saracco and J. Vercruysse, Partial and global representations of finite groups, arXiv:2005.09465
    P. Saracco and J. Vercruysse, Globalizations of geometric partial actions, arXiv:2001.07669.
  • Accepted for publication/in press

    M.Buckley, T. Fieremans, C. Vasilakopoulou and J. Vercruysse, Oplax Hopf algebras, preprint arXiv:1710.01465, to appear in Higher Structures, 2021
    A. Agore, A. Gordienko and J. Vercruysse, Equivalences of (co)module algebra structures over Hopf algebras, preprint arXiv:1812.04563, to appear in J. Noncommut. Geom., 2021.
  • Published

    [31] G. Böhm, J. Vercruysse, BiHom Hopf algebras viewed as Hopf monoids, arXiv preprint arXiv:2003.08819, Contemporary Mathematics 771 (2021), 141.
    [30] M.M.S. Alves, E. Batista, F. Castro, G. Quadros and J. Vercruysse, partial corepresentations of Hopf algebras,  J. Algebra 577 (2021), 74–135. 
    [29] M. Buckley, T. Fieremans, C. Vasilakopoulou and J. Vercruysse, A Larson-Sweedler theorem for Hopf V-categories, Adv. Math. 376 (2021), 107456.
    [28] J. Hu and J. Vercruysse, Geometrically partial actions, Trans. Amer. Math. Soc., 373 (2020), 4085–4143.
    [27] M.M.S. Alves, E. Batista and J. Vercruysse, Dilations of partial representations of Hopf algebras, J. Lond. Math. Soc. 100 (2019), 273–300.
    [26] M. Gran, F. Sterck and Joost Vercruysse, A semi-abelian extension of a theorem by Takeuchi, J. Pure Appl. Algebra 223 (2019), 4171–4190.
    [25] M. Gran, G. Kadjo and J. Vercruysse, Split extension classifiers in the category of cocommutative Hopf algebras, Bull. Belg. Math. Soc. Simon Stevin 25 (2018), 355–382.
    [24] S. Caenepeel, E. Batista and J. Vercruysse, Hopf categories, Algebr. Represent. Theory, 19 (2016), 1173–1216.
    [23] M. Gran, G. Kadjo and J. Vercruysse, A Torsion Theory in the Category of Cocommutative Hopf Algebras, Appl. Categ. Structures, 24 (2016) 269–282.
    [22] E. Batista and J. Vercruysse, Dual constructions for partial actions of Hopf algebras, J. Pure Appl. Algebra 220 (2016), 518--559.
    [21] M.M.S. Alves, E. Batista and J. Vercruysse, Partial representations of Hopf algebras, J. Algebra 426 (2015).
    [20] I. Goyvaerts and J. Vercruysse, Lie monads and dualities, J. Algebra 414 (2014), 120--158.
    [19] I. Goyvaerts and J. Vercruysse, On the duality of generalized Lie and Hopf algebras, On the duality of generalized Lie and Hopf algebras, Adv. Math. 258 (2014), 154--190.
    [18] J. Vercruysse, Hopf algebras -- Variant notions and reconstruction theorems, in ``Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse'', C. Heunen, M. Sadrzadeh, E. Grefenstette (eds.). Oxford University Press, Oxford, 2013, 115--145.
    [17] I. Goyvaerts and J. Vercruysse, A note on the categorisation of Lie algebras, in ``Lie Theory and its applications in physics IX'', V. Dobrev (eds.), Spring Proceedings in Mathematics and Statistics 36, Springer, Tokyo, 2013, 541--550.
    [16] T. Brzezinski, A. Vazquez Marquez and J. Vercruysse, The Eilenberg-Moore category and a Beck-type theorem for a Morita context, Appl. Categorical Structures 19, (2011), 821--858.
    [15] K. Janssen and J. Vercruysse, Multiplier Hopf and bi-algebras, J. Algebra Appl. 9 (2), (2010), 275 -- 303.
    [14] F. Castaño Iglesias, C. Nastasescu, J. Vercruysse, Quasi-Frobenius functors. Applications, Comm Algebra, 38 (8), (2010), 3057-3077.
    [13] G. Böhm and J. Vercruysse, Morita theory for comodules over corings, Comm Algebra. 37 (9), (2009), 3207 -- 3247.
    [12] T. Brzezinski and J. Vercruysse, Bimodule Herds, J. Algebra, 321 (9), (2009), 2670--2704.
    [11] L. El Kaoutit and J. Vercruysse, Cohomology for Bicomodules. Separable and Maschke Functors, Journal of K-theory, 3 (1) (2009), 123--152.
    [10] J. Vercruysse, Quasi-co-Frobenius corings as Galois comodules, Arabian Journal for Science and Engeneering, 22 (2C) (2008), 529--552.
    [9] J. Vercruysse, Equivalences between categories of Modules and categories of Comodules, Acta Math. Sin. (Engl. Ser.) 24 (10) (2008), 1655--1674.
    [8] M. Iovanov and J. Vercruysse, Cofrobenius Corings and adjoint Functors, Journal of Pure and Applied Algebra, 212 (9), 2027-2058 (2008).
    [7] J. Gómez-Torrecillas and J. Vercruysse, Comatrix Corings and Galois Comodules over firm rings, Algebras and Representation Theory, 10 (3) (2007), 271--306.
    [6] G. Böhm and J. Vercruysse, Morita theory for Coring extensions and Cleft bicomodules, Advances in Mathematics 209 (2007), 611--648. Corrigendum, Advances in Mathematics 221 (2009), 682--686.
    [5] S. Caenepeel, E. De Groot and J. Vercruysse, Galois theory for Comatrix Corings: Descent theory, Morita theory, Frobenius and separability properties, Trans. Amer. Math. Soc. 359 (2007), 185--226.
    [4] S. Caenepeel, E. De Groot and J. Vercruysse, Constructing Infinite Comatrix Corings from Colimits, Appl. Categorical Structures, 14 (2006), 539--565.
    [3] J. Vercruysse, Local units versus local projectivity. Dualisations : Corings with local structure maps, Communications in Algebra 34 (2006), 2079--2103.
    [2] S. Caenepeel, J. Vercruysse and Shuanhong Wang, Rationality properties for Morita contexts associated to corings, in ``Hopf algebras in non-commutative geometry and physics", Caenepeel S. and Van Oystaeyen, F. (eds.), Lect. Notes Pure Appl. Math., Dekker, New York (2005) 113--136.
    [1] S. Caenepeel, J. Vercruysse and Shuanhong Wang, Morita Theory for corings and cleft entwining structures, Journal of Algebra 276 (2004) 210--235.
  • Edited volumes
    S. Caenepeel, M. Gran, J. Vercruysse, Y. Zhang (eds.), “New trends in Hopf algebras and tensor categories”, Bull. Belgian Math. Soc. - Simon Stevin 23 (2016) issue 5, ISSN 1370-1444.
    S. Caenepeel, M. Gran, J. Vercruysse, Y. Zhang (eds.), “New trends in Hopf algebras and tensor categories (Part II)”, Bull. Belgian Math. Soc. - Simon Stevin 24 (2017) issue 1, ISSN 1370-1444.

Projects

  • CDR (Crédit de recherche) by FNRS | Coactions of generalized Hopf algebras (Ref. J.0061.13 CDR FRFC) | EUR 6500 | 2013-2014
  • ARC consolidator grant by FWB | Hopf algebras and the symmetries of non-commutative spaces | EUR 200 000 | 2015-2018
  • MIS (Incentive grant for research) by FNRS | Actions in Non-commuTatIve algebra and Partial mODulEs (ANTIPODE) | EUR 286 000 | 2018-2021
  • ARC advanced grant by FWB | joint with Michele D'Adderio, Dimitri Leemans and Spela Spenko | EUR 663 381 | 2021-2024
  • Fonds Thelam (Foundation Roi Baudeouin) | Partial Symmetries of Non-Commutative Spaces | EUR 25 000 | 2021-2024

Conferences and workshops

  • Future events
    Second antipode workshop | Brussels (ULB) | was planned September 2020 but postponed due to Covid-19
  • Past events
    Hopf algebra Workshops | joint workshops by VUB and ULB | January 31, March 19 and April 17 2012
    New trends in Hopf algebras and tensor categories | Brussels | June 2-5 2015
    Brauer groups, Hopf algebras and monoidal categories | conference in Honour of Stef Caenepeel’s 60th birthday | Turin | May 24-27 2016
    Hopf algebras @ Brussels | Brussels (ULB) | September 28-29 2016
    Séminaire Itinérante de Catégories (SIC) | Brussels (ULB) | January 27 2017
    Brussels Hopf algebra workshop | Brussels (ULB) | August 29-30 2017
    First antipode workshop | Brussels (ULB) | 19-10 March 2018
    Aspects of Higher representation theory: quantum groups and categorification | Brussels (VUB) | 21-25 January 2019

Seminars

Teaching

Students can find info and lecture notes on each of the courses I teach via the UV-page.

Courses (2020-21)

  • MathF102
    Algèbre Linéaire et Géométrie: aspects théoriques et algorithmiques | BA Mathématique | bloc 1
  • MathF3003
    Algèbre et géométrie II | BA Mathématique | bloc 3
  • MathS202
    Mathématique: algèbre linéaire II et fonctions de plusieurs de variables | BA Ingénieur de gestion | bloc 2
  • MathF407
    Groupes, algèbres et représentations | MA Mathématique
  • MathF519
    Algèbre catégorique | MA Mathématique

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