Dion Coumans' homepage

Having obtained my PhD at the Radboud University Nijmegen in the Algebra & Logic group, supervised by Mai Gehrke and Ieke Moerdijk, I now have a teaching position at that same university.

Contact details

Radboud Universiteit Nijmegen
FNWI, IMAPP
P.O. Box 9010
6500 GL Nijmegen
The Netherlands

You can visit me at:
Huygensgebouw
Room HG03.065
Heyendaalseweg 135
6525 AJ Nijmegen

Or contact me by phone or mail:
T: +31-(0)24-3653220
E: coumans at math.ru.nl

Research

My current research interest is in duality theory, relational semantics and categorical logic. In particular, I am working on extending techniques used in the algebraic study of propositional logics to the categorical setting, so that that they can be applied in the study of predicate logics.

Scientific texts

• Canonical extensions in logic - some applications and a generalisation to categories, PhD thesis supervised by prof. M. Gehrke and prof. I. Moerdijk.
  
• Generalising canonical extension to the categorical setting. In: Annals of Pure and Applied Logic
  
• Relational semantics for full linear logic, with Mai Gehrke and Lorijn van Rooijen. To appear in: Journal of Applied Logic, special issue 'Logic, categories, semantics' [preprint].
  
• On generalizing free algebras for a functor, with Sam van Gool. In: Journal of Logic and Computation.
  
• Relational semantics for a fragment of linear logic. To appear in: Future Directions of Logic, Proceedings of PhDs in Logic III [preprint].
  
• Constructing the Lindenbaum algebra for a logic step-by-step using duality, with Sam van Gool. Extended version of a paper by Sam van Gool, which is to appear in the proceedings of PhDs in Logic III.
  
• Scalars, monads and categories, with Bart Jacobs, Arxiv preprint.
  
• Distributive lattice-structured ontologies, with Hans Bruun and Mai Gehrke. In: the proceedings of CALCO 2009, LNCS, volume 5728, p. 267-283.
  
• The right choice? - An intuitionistic exploration of Zermelo's axiom, Master's thesis at Radboud University Nijmegen under supervision of Wim Veldman.
  
• Oneindige spelen, Bachelor's thesis at Radboud University Nijmegen under supervision of Wim Veldman [in Dutch].
  

Other texts

• Positiestelsels, rekenen en streepjescodes, with Mai Gehrke and Lorijn van Rooijen, material for high school students [in Dutch].
  
• Wiskundetoernooi 2008: wat kun je nu eigenlijk met wiskunde?, with Mirte Dekkers and Klaas Landsman. In: Nieuwe Wiskrant 28, 2008, p. 12-14 [in Dutch].
  
• A random walk down Wall Street, with Janneke van den Boomen, Ruben van den Brink, Klaas Landsman en Daan Wanrooy. In: Nieuw Archief voor Wiskunde 5/9, 2008, p. 18-23 [in Dutch].
  

Talks

• On constructing free algebras and properties of free Heyting algebras, Category Theory Seminar, Cambridge (November 2012) [slides]
  
• Construction of free algebras via a functor on partial algebras, Duality Theory in Algebra, Logic and Computer Science, Oxford (August 2012) [slides]
  
• Canonical extension in first-order logic and Makkai's topos of types, Topological Methods in Logic III, Tbilisi (July 2012) [slides]
  
• Duality theory in modal logic, tutorial at Topological Methods in Logic III, Tbilisi (July 2012)
  
• Canonical extension for categories and Makkai's topos of types, Seminaire Itinerant de Categories, Louvain-la-Neuve (May 2012) [slides]
  
• Generalizing canonical extension to the categorical setting, PSSL 93, Cambridge (April 2012) [slides]
  
• Construction of free modal algebras - an application of duality theory, Ph.D. Colloquium, Nijmegen (March 2012)
  
• Generalizing canonical extension to the categorical setting, DIAMANT symposium, Elspeet (November 2011) [slides]
  
• On generalizing canonical extension, Radboud Category Theory Seminar, Nijmegen (November 2011) [slides]
  
• Generalizing canonical extension to the categorical setting, Workshop on Aspects of Duality Theory, Oxford (August 2011) [slides]
  
• Free algebras via a functor on partial algebras, Topology, Algebra and Categories in Logic (TACL), Marseille (July 2011) [slides]
  
• Canonical extension of coherent categories, Topology, Algebra and Categories in Logic (TACL), Marseille (July 2011) [slides]
  
• Defining a notion of canonical extension for coherent categories, McGill Category theory seminar, Montreal (March 2011)
  
• Relational semantics for a fragment of linear logic, PhDs in Logic III, Brussels (February 2011) [slides]
  
• Weet jij het zeker?, Science Symposium, Raayland College Venray (January 2011) [slides]
  
• Finitely generated free algebras and duality DIAMANT/EIDMA Symposium, Lunteren (November 2010) [slides]
  
• Semantics and duality (joint talk with Mai Gehrke) Workshop on logic, categories and semantics, Bordeaux (November 2010) [slides]
  
• Duality for classical first order logic, PhD-colloquium, Nijmegen (June 2010) [slides]
  
• Duality for classical first order logic, Mathematical Logic in the Netherlands, Utrecht (May 2010) [slides]
  
• Scalars, monads and categories, groupe de travail Catégories supérieures, polygraphes et homotopie, Paris (March 2010)
  
• Positiestelsels, rekenen en streepjescodes, OMO-docentendag, Tilburg (November 2009) [slides]
  
• Distributive lattice-structures ontologies, Conference on Algebra and Coalgebra in Computer Science, Udine (September 2009) [slides]
  
• Knowledge Representation - een toepassing van dualiteitentheorie, PhD-colloquium, Nijmegen (March 2009)
  
• Distributive lattice-structures ontologies, Algebra | Coalgebra seminar, Amsterdam (March 2009)
  

Teaching

I have been / will be teaching the courses

• Ringen en Lichamen - spring 2013
• Analyse 1 - spring 2013
• Wiskunde 2 voor informatici - spring 2013
• Getallen - fall 2012
• Lineaire algebra voor scheikundigen - fall 2012
• Wiskunde 2 voor kunstmatige intelligentie - fall 2012
• Analyse 1 - spring 2012

I have been teaching exercises classes on

• Getallen - fall 2011
• Getallen - fall 2010
• Lattice Theory - fall 2009
• Universal Algebras - spring 2009