Maître de Conférences (with Habilitation à Diriger des Recherches) at the Laboratory for Pure and Applied Mathematics of the Université du Littoral-Côte d'Opale.
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Postal address:
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Bio - Publications - Conferences - Study leaves
July 1, 1998 : ''Licentiaat in de wiskunde'' with dissertation entitled ''Quantaloids of operational resolutions and state transitions'', supervisors: D. Aerts and B. Coecke, Vrije Universiteit Brussel, Belgium.
1998 - 2005 : Research and teaching assistant for the mathematics department at the Université Catholique de Louvain, Belgium.
July 1, 1999 : ''Diplôme d'études approfondies en mathématiques'' with disseration entitled ''Physics and Categories'', supervisor: F. Borceux, Université Catholique de Louvain, Belgium.
November 12, 2003 : ''Docteur en mathématiques'' (PhD) with dissertation entitled ''Categorical structures enriched in a quantaloid: categories and semicategories'', supervisor: F. Borceux, Université Catholique de Louvain, Belgium. [download pdf]
2005 - 2006 : Post-doctoral researcher at the Centre for Mathematics of the Universidade de Coimbra, Portugal.
2006 - 2009 : Post-doctoral Fellow of the Flemish Research Foundation (FWO) at the department of mathematics and computer science of the Universiteit Antwerpen, Belgium.
2009 : Maître de Conférences at the Université du Littoral-Côte d'Opale, France.
December 12, 2011 : ''Habilitation à diriger des recherches'' with dissertation entitled ''On quantaloid-enriched categories in general, and sheaves on a quantaloid in particular'' [download pdf]
(All PDFs provided below are preprints. The authoritative versions of these papers are always the published ones.)
1998 : (with H. Amira and B. Coecke) ''How quantales emerge by introducing induction within the operational approach", Helvetica Physical Acta 71, 554-572. [download pdf] [journal's web site]
1999 : "Physics and Categories: The Geneva School approach to the axiomatic foundations of physics", excerpt from DEA dissertation. [download pdf]
1999 : (with B. Coecke) ''Operational resolutions and state transitions in a categorical setting", Foundations of Physics Letters 12, 29-49. [download pdf] [journal's web site]
1999 : (with B. Coecke) ''Duality of quantales emerging from an operational resolution", International Journal of Theoretical Physics 38, 3269-3281. [download pdf] [journal's web site]
2000 : (with B. Coecke) ''State transitions as morphisms for complete lattices", International Journal of Theoretical Physics 39, 601-610. [download pdf] [journal's web site]
2000 : (with F. Borceux) ''Short introduction to enriched categories'', chapter in: Current research in operational quantum logic: algebras, categories, languages (edited by B. Coecke, D. Moore and A. Wilce), Fundamental Theories of Physics 111, Kluwer Academic Publishers, 167-194. [download pdf] [publisher's web site]
2001 : ''Logique Quantique Opérationelle et Catégories", Compte-Rendu du Séminaire Itinérant des Catégories 18. [download pdf]
2001 : (with B. Coecke and D. Moore) ''Quantaloids describing propagation of physical properties", Foundations of Physics Letters 14, 133-145. [download pdf] [journal's web site]
2003 : (with S. Sourbron, R. Luypaert and M. Osteaux) ''Discretising the convolution product in DCI-MRI based quantification of CBF'', Magnetic Resonance Materials in Physics, Biology and Medicine (MAGMA) 16, s134-s135. [journal's web site]
2003 : ''Introduction to 'Categorical structures enriched in a quantaloid: categories and semicategories''', excerpt from PhD thesis. [download pdf]
2005 : ''Categorical structures enriched in a quantaloid: categories, distributors, functors'', Theory and Applications of Categories 14, 1-45. [download pdf] [journal's web site]
2005 : ''Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories'', Cahiers de Topologie et Géométrie Différentielle Catégoriques 46, 99-121. [download pdf] [journal's web site]
2005 : ''Categorical structures enriched in a quantaloid: orders and ideals over a base quantaloid'', Applied Categorical Structures 13, 235-255. [download pdf] [journal's web site]
2005 : ''The canonical topology on a meet-semilattice'', International Journal of Theoretical Physics 44, 2283-2293. [download pdf] [journal's web site]
2006 : ''Towards 'dynamic domains': totally continuous cocomplete Q-categories (Extended Abstract)'', Electronic Notes in Theoretical Computer Science 155, 617-634. [download pdf] [journal's web site]
2006 : ''Categorical structures enriched in a quantaloid: tensored and cotensored categories'', Theory and Applications of Categories 16, 283-306. [download pdf] [journal's web site]
2007 : ''Towards 'dynamic domains': totally continuous cocomplete Q-categories'', Theoretical Computer Science 373, 142-160. [download pdf] [journal's web site]
2007 : ''Q-modules are Q-suplattices'', Theory and Applications of Categories 19, 50-60. [download pdf] [journal's web site]
2007 : (with B. Van Steirteghem) ''Propositional systems, Hilbert lattices and generalized Hilbert spaces'', chapter in: Handbook of Quantum Logic and Quantum Structures: Quantum Structures (edited by K. Engesser, D. M. Gabbay and D. Lehmann), Elsevier, 477-524. [download pdf] [publisher's web site]
2009 : (with M. M. Clementino and D. Hofmann) ''Exponentiable functors between quantaloid-enriched categories'', Applied Categorical Structures 17, 91-101. [download pdf] [journal's web site]
2009 : (with H. Heymans) ''On principally generated Q-modules in general, and skew local homeomorphisms in particular'', Annals of Pure and Applied Logic 161, 43-65. [download pdf] [journal's web site]
2009 : (with H. Heymans) ''Modules on involutive quantales: canonical Hilbert structure, applications to sheaves'', Order 26, 177-196. [download pdf] [journal's web site]
2010 : '''Hausdorff distance' via conical cocompletion'', Cahiers de Topologie et Géométrie Différentielle Catégoriques 51, 51-76. [download pdf] [journal's web site]
2011 : (with D. Hofmann) ''Towards Stone duality for topological theories'', Topology and its Applications 158, 913-925. [download pdf] [journal's web site]
2011 : (with H. Heymans) ''Symmetry and Cauchy completion of quantaloid-enriched categories'', Theory and Applications of Categories 25, 276-294. [download pdf] [journal's web site]
2011 : (with H. Heymans) ''Elementary characterisation of quantaloids of closed cribles'', Journal of Pure and Applied Algebra, to appear, 13 pages. [download pdf] [journal's web site]
2011 : (with H. Heymans) ''Allegories of enriched categories'', submitted, 27 pages. [download pdf]
June 1998 : Talk : ''Operational resolutions and state transitions in a quantaloid setting'', International workshop on current research in operational quantum logic, Brussels, Belgium.
September 1998 : Talk : ''A duality of quantales describing structure preservance for generalized states'', fourth biannual IQSA meeting, Liptovski Jan, Slovakia.
Early May 1999 : Talk : ''On resolutions, state/property transitions, and the enriched categories they constitute'', International workshop on current research in operational quantum logic, Brussels, Belgium.
End of May 1999 : Talk : (with B. Coecke (speaker) and D. Moore) ''Dualities of quantaloids describing propagation of physical properties", Workshop on categorical methods in algebra and topology, organized by F. Borceux in Nassogne, Belgium.
July 1999 : Talk : (with B. Coecke (speaker) and D. Moore) ''Quantaloids describing propagation of physical properties", Category Theory 99, Coimbra, Portugal.
August 1999 : Talk : ''Why the category of sup-lattices may be of interest to physicists'', Australian category theory seminar, Sydney, Australia.
October 1999 : Participation : 71th meeting of the Peripatetic Seminar on Sheaves and Logic, Louvain-la-Neuve, Belgium.
November 1999 : Talk : ''The Geneva School approach to the axiomatic foundations of physics'', Séminaire des doctorants, Dépt. de Mathématique de l'UCL, Belgique.
April 2000 : Co-organization : Peripatetic seminar on sheaves and logic 72, a.ka. Category Theory Symposium as satellite to the International workshop on current research in operational quantum logic, Brussels, Belgium.
April 2000 : Talk : ''Categorical methods in operational quantum logic'', Peripatetic seminar on sheaves and logic 72, a.ka. Category Theory Symposium as satellite to the International workshop on current research in operational quantum logic, Brussels, Belgium.
July 2000 : Poster : (with B. Coecke and D. Moore) ''(Categorical) Quantum Process Semantics'', Category Theory 2000, Como, Italy. [www]
Early November 2000 : Participation : 74th meeting of the Paripathetic Seminar on Sheaves and Logic, Cambridge, UK.
November 2000 : Talk : ''Logique Quantique Opérationelle et Catégories", Séminaire Itinérant des Catégories, Université de Picardie-Jules Verne, Amiens, France. [www]
April 2001 : Talk : ''A corestriction of the Yoneda embedding as frame completion of a bounded poset with finite meets, with an appication to quantum logic", sixth biannual IQSA meeting, Cesenatico, Italy. [see elsewhere on this page for notes on this lecture: ''The canonical topology on a meet-semilattice'']
End of May 2001 : Participation : Workshop on semi-abelian categories, organized by F. Borceux at Haute-Bodeux, Belgium.
October 2001 : Talk : ''Si une catégorie cartésienne fermée est *-autonome pour cette même structure monoïdale, elle est une algèbre de Boole", Séminaire des doctorants, Département de Mathématique de l'UCL, Belgique.
November 2001 : Talk : ''What can we certainly say about what may possibly be? The operational resolution, quantales of induced state/property transitions, and causal duality as crux of the biscuit", Comlab's Lunchtime Meeting, Oxford, UK.
Mid June 2002 : Series of 3 Talks : ''Quantaloid-enriched (semi)categories, distributors and functors", Séminaire de Catégories, Dépt. de Mathématique de l'UCL, Belgique.
Early July 2002 : Poster : (with Steven Sourbron) ''Causal duality: what it is, and what it is good for", sixth biannual IQSA meeting, Vienna, Austria. [www]
Mid July 2002 : Talk : ''Quantaloid-enriched (semi)categories, distributors and functors: an overview", Meeting on the Theory and Applications of Quantales, Instituto Superior Técnico, Lisbon, Portugal. [www]
End of September 2002 : Participation : Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, organized at the Fields Institute, Toronto, Canada. [www]
January 2003 : Talk : ''Totally regular semicategories enriched in a quantaloid: from Louvain-la-Neuve to Sydney and back'', Australian Category Seminar, Sydney, Australia.
January 2003 : Talk : ''The principle of Causal Duality establishes quantum logics with (external) implication as quantaloid-enriched categories'', Australian Category Seminar, Sydney, Australia.
Early March 2003 : Series of 3 Talks : ''Semicatégories enrichies dans un quantaloïde'', Séminaire de Catégories, Dépt. de Mathématique de l'UCL, Belgique.
Late March 2003 : Talk : ''Causal Duality for processes as (co)tensors in a quantaloid enriched category'', Workshop ''Seminarie: Logica & Informatica 2003'', Brussels, Belgium. [www]
Mid May 2003 : Participation : Séminaire Itinérant des Catégories (Journée en l'honneur d'Yves Diers), Université de Valenciennes et du Hainaut Cambrésis, Valenciennes, France. [www]
Early September 2003 : Talk : ''Ideals, orders and sets over a base quantaloid'', European Category Theory Meeting, Haute-Bodeux, Belgium.
Mid September 2003 : Poster : (with S. Sourbron, R. Luypaert and M. Osteaux) ''Discretising the convolution product in DSC-MRI based quantification of CBF'', poster presented by S. Sourbron at the 20th Annual Scientific Meeting of the European Society for Magnetic Resonance in Medicine and Biology (ESMRMB), Rotterdam, The Netherlands. [www]
June 2004 : Participation : Séminaire Itinérant des Catégories, Université du Littoral Côte d'Opale, Dunkerque, France. [www]
June 2004 : Invited talk : ''Order! Order in the House!'', Oxford University's Computing Laboratory, Oxford, United Kingdom.
July 2004 : Talk : ''Orders and ideals over a base quantaloid", Category Theory 04, Vancouver, Canada. [www]
November 2004 : Participation : Séminaire Itinérant des Catégories, Université de Paris 7, Paris, France. [www]
December 2004 : Participation : Workshop on Mathematical Structures in Quantum Computing (Q-day I), Institut de mathématiques de Jussieu, Université de Paris 7, Paris, France.
January 2005 : Talk : ''Ordered sheaves on a quantaloid'', Workshop on Logic from Quantales, Oxford University's Computing Laboratory, Oxford, United Kingdom. [www]
January 2005 : Talk : ''Dynamic domains'', Mathematics Institute, Oxford University, Oxford, United Kingdom. [www]
Early February 2005 : Talk : ''Omega-verzamelingen'', Departement Wiskunde, Vrije Universiteit Brussel, Brussels, Belgium.
Early March 2005 : Talk : ''Q-catégories totalement continues'', Séminaire de Catégories, Dépt. de Mathématique de l'UCL, Belgique. [www]
Mid May 2005 : Participation : Séminaire Itinérant des Catégories, Université du Littoral Côte d'Opale, Calais, France. [www]
Mid May 2005 : Talk : ''Towards 'dynamic domains': totally continuous cocomplete Q-categories'', Twenty-First Conference on the Mathematical Foundations of Programming Semantics (MFPS XXI), University of Birmingham, Birmingham, United Kingdom. [www]
May-June 2005 : Participation : Summer School on Topos Theory, Haute-Bodeux, Belgium. [www]
September 2005 : Talk : ''Categorical structures enriched in a quantaloid: results, projects, ideas and dreams'', Algebra Seminar, Centro de Matemática da Universidade de Coimbra, Portugal. [www]
November 2005 : Talk : ''Q-modules are precisely Q-suplattices'', Category Theory Seminar, Centro de Matemática da Universidade de Coimbra, Portugal. [www]
December 2005 : Talk : ''Q-modules are precisely Q-suplattices'', Workshop on Mathematical Structures in Quantum Computing (Q-day II), Institut Henri Poincaré, Paris, France. [www]
February 2006 : Talk (popularizing) : ''Over de dimensie van een ruimte'', Artefact Festival, STUK, Leuven, Belgium. [www]
March 2006 : Talk : ''Abstract projective geometry and the origin of the logico-algebraic approach to quantum theory'', Algebra Seminar, Centro de Matemática da Universidade de Coimbra, Portugal. [www]
June 2006 : Talk : ''Q-modules are Q-suplattices'', Algebra Seminar, Instituto Superior Técnico, Lisbon, Portugal.
June-July 2006 : Talk : ''Q-modules are Q-suplattices'', Category Theory 06, Halifax, Canada. [www]
July 2006 : Talk : ''Abstract projective geometry and Piron's representation theorem'', Cats, Kets and Cloisters, University of Oxford, Oxford, United Kingdom. [www]
September 2006 : Participation : New techniques in Hopf algebras and graded ring theory, Brussels, Belgium.
November 2006 : Participation : Séminaire Itinérant des Catégories, Université du Littoral Côte d'Opale, Calais, France. [www]
Mid May 2007 : Participation : Third Workshop on Formal Topology, Accademia Galileiana di Scienze Lettere e Arti, Padua, Italy. [www]
Mid May 2007 : Talk : ''Exponentiability in Cat(Q)'', Algebra Seminar, Department of Algebra and Geometry, Masaryk University, Brno, Czech Republic.
Early June 2007 : Participation : Summer School on Contemporary Categorical Methods in Algebra and Topology, Haute-Bodeux, Belgium. [www]
Mid June 2007 : Participation : Category Theory 07, Carvoeiro, Portugal. [www]
Early July 2007 : Invited talk : ''Dynamic logic: a non-commutative topology of truth values'', Seminar on mathematical aspects of novel approaches to quantum theory and foundations of physics, organized by Basil Hiley and Georg Wikman (SHIRD), Åskloster, Sweden.
Early August 2007 : Talk : ''Sheaves on non-commutative topologies'', Categorical Quantum Logic, Oxford, UK. [www]
Early September 2007 : Participation : ''Journées Jean-Yves Girard'', Institut Henri Poincaré, Paris, France. [www]
Late September 2007 : Participation : Noncommutative rings and geometry (Conference in honour of Fred Van Oystaeyen's 60th birthday), Almerìa, Spain. [www]
November 2007 : Talk : ''Principally generated Q-modules'', Departement Wiskunde, Vrije Universiteit Brussel, Brussels, Belgium.
November 2007 : Talk : ''Principally generated Q-modules'', Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal.
January 2008 : Participation : Categories, Logic and Foundations of Physics, Imperial College, London, United Kingdom. [www]
January 2008 : Participation : Commentator for Klaas Landsman's lecture on ''The principle of general tovariance'', Symposium on Logic and Physics, Universiteit Utrecht, Utrecht, The Netherlands. [www]
February 2008 : Talk : ''Totally continuous and totally algebraic cocomplete Q-categories'', Australian Category Seminar, Sydney, Australia. [www]
February 2008 : Talk : ''Locally principally generated Q-modules'', Australian Category Seminar, Sydney, Australia. [www]
March 2008 : Talk : ''Skew local homeomorphisms'', Australian Category Seminar, Sydney, Australia. [www]
March 2008 : Talk : ''Exponentiable functors between quantaloid-enriched categories'', Australian Category Seminar, Sydney, Australia. [www]
June 2008 : Talk : ''Principally generated modules on a quantaloid'', Category Theory 08, Calais, France. [www]
Early September 2008 : Two invited talks: ''Principally generated quantaloid-modules'' and ''Skew local homeomorphisms'', Workshop on Sheaves in Geometry and Quantum Theory, Radboud Universiteit Nijmegen, the Netherlands. [www]
Mid September 2008 : Participation : QICS Workshop on Foundational Structures for Quantum Information and Computation, Universitätszentrum Obergurgl, University of Innsbruck, Austria. [www]
Mid October 2008 : Co-organisation and Talk : ''Skew local homeomorphisms'', Categories in Algebra, Geometry and Logic, A tribute to the work of Francis Borceux and Dominique Bourn on the occasion of their sixtieth birthday, Royal Academy of Sciences, Brussels, Belgium. [www]
Early Januray 2009 : Invited talk : ''Principally generated modules on a quantale'', Fourth Workshop on Categories, Logic and Foundations of Physics (CLAP IV), Imperial College, London, United Kingdom. [www]
Mid March 2009 : Talk : '''Hausdorff distance' via conical cocompletion'', Département de Mathématiques, Université Catholique de Louvain, Belgium.
Mid March 2009 : Talk : ''Enriched colimits vs. suprema'', Institute for Mathematics, Astrophysics and Particle Physics, Radboud Universiteit Nijmegen, the Netherlands.
June-July 2009 : Participation : Category theory 2009, Cape Town, South-Africa. [www]
July 2009 : Invited talk : ''Sheaves as modules'', Seminar on novel mathematical structures in physics: non-commutative geometry, organized by Basil Hiley and Georg Wikman (SHIRD), Åskloster, Sweden. [www]
December 2009 : Participation : 89th meeting of the Paripathetic Seminar on Sheaves and Logic, Louvain-la-Neuve, Belgium. [www]
March 2010 : Participation : Séminaire Itinérant des Catégories, Université de Paris 7, Paris, France. [www]
June 2010 : Invited talk : "Symétrie et Cauchy complétion", Séminaire Itinérant des Catégories, Université de Picardie-Jules Verne, Amiens, France. [www]
June 2010 : Talk : "Symmetry and Cauchy-completion of quantaloid-enriched categories", Category Theory 2010, Genova, Italy. [www]
August 2010 : Invited talk : "Characterisation of commutative topologies amongst non-commutative topologies", International workshop on noncommutative algebra, Shaoxing, China.
November 2010 : Co-organisation : Séminaire Itinérant des Catégories, Université du Littoral-Côte d'Opale, Calais, France. [www]
March 2011 : Participation : Séminaire Itinérant des Catégories, Université Diderot Paris 7, Paris, France. [www]
May 2011 : Invited talk : "An elementary characterisation of quantaloids of closed cribles", Category Theory, Algebra and Geometry, a conference on the occasion of Ross Street's Chaire de la Vallée Poussin, Département de Mathématiques, Université Catholique de Louvain, Belgium. [www]
June 2011 : Participation : Colloquium in Honour of Jean Bénabou, Ecole Normale Superieure, Paris, France. [www]
July 2011 : Participation : Fifth International Conference on Topology, Algebra and Categories in Logic (TACL 2011), Marseille, France. [www]
October 2011 : Co-organisation and talk : "Faisceaux déguisés en modules", Séminaire Itinérant des Catégories, Université du Littoral-Côte d'Opale, Calais, France. [www]
Mid December 2011 : Invited talk : ''Axioms for quantaloids of closed cribles'', Algebra Seminar, Department of Algebra and Geometry, Masaryk University, Brno, Czech Republic.
February 2012 : Invited talk : "Quantaloid-enriched categories for multi-valued logic and other purposes", 33rd Linz Seminar on Fuzzy Set Theory, Linz, Austria. [www]
April 2012 : Participation : 93rd meeting of the Paripathetic Seminar on Sheaves and Logic, Cambridge, UK. [www]
May 2012 : Participation : Séminaire Itinérant des Catégories, Université de Louvain, Louvain-la-Neuve, Belgique. [www]
June 2012 : Invited talk : "TBA", 1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Liège, Belgium. [www]
June 2012 : Talk : "Nombreux nombres: du naturel au complexe", Stage pour élèves du lycée, Université du Littoral-Côte d'Opale, Calais, France.
June 2012 : Talk : "TBA", Oxford Advanced Seminar on Informatic Structures, Oxford University, UK. [www]
Early July 1999 : 1 week at the Dipartimento di Matematica at the Università degli Studi Roma Tre, Italy.
August-September-October 1999 : 10 weeks at the School of Mathematics and Statistics at the University of Sydney, Australia.
January 2003 : 5 weeks at the Division of Information and Communication Sciences at Macquarie University in Sydney, Australia.
June 2004 : 1 week at Oxford University's Computing Laboratory in Oxford, United Kingdom.
Early April 2005 : 1 week at Programmes, Preuves, Systèmes, Institut de mathématiques de Jussieu, Université de Paris 7, Paris, France.
Mid May 2006 : 3 days at Instituto Superior Técnico, Lisbon, Portugal.
Mid May 2007 : 1 week at the Department of Algebra and Geometry, Masaryk University, Brno, Czech Republic.
Late November 2007 : 1 week at the Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal.
February-March-April 2008: 8 weeks at the Division of Information and Communication Sciences at Macquarie University in Sydney, Australia.
May 2008 : 1 week at the Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal.
January 2010 : 3 days at Oxford University's Computing Laboratory in Oxford, United Kingdom.
August 2010 : 2 weeks at Shaoxing University, China.
Mid December 2011 : 1 week at the Department of Algebra and Geometry, Masaryk University, Brno, Czech Republic.