Projects per year
Organization profile
Organisation profile
The research team investigates mathematical structures that are important in several basic areas of mathematics like geometry, representation theory, functional analysis, differential calculus or theory of approximation. The motivation also comes from outside mathematics, from computer science or physics where some of the mathematical structures that are studied are called upon as models. By application of methods from category theory the relation between these mathematical structures is studied. The compatibility of their fundamental constructions is investigated and a general study of their representability, as well as of their function space theory is undertaken. More specifically the theory of frames or locales uses ordertheoretic notions to gain more insight in topological structures and to shed light on the use of choice principles in topology (or sometimes simply avoid them altogether). The theory of approach spaces provides the tools for obtaining quantified results in topology and in functional analysis, extending the isometric theory of Banach spaces. The team contributes to the development of the theory of semiabelian categories and tensor categories Semiabelian categories allow a unified setting for many important homological properties of nonabelian categories. Categories of quantum groups, of rings, of Liealgebras and of crossed modules are typical nonabelian categories, often with a tensor structure. Abstract tensor categories lead to interesting noncommutative spaces (operator algebras) whose analytical properties are studied in connection with the properties of the associated category. The main emphasis is on representation categories of quantum deformations of semisimple Lie groups.
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Projects
 6 Finished

OZR1424: Further development of semiabelian homology theory
Kieboom, R. & Van Der Linden, T.
1/01/07 → 31/12/07
Project: Fundamental



OZR431: Application of methods from categorical topology in order to solve problems in the completion theory of quasiduniform spaces.
1/01/00 → 31/12/01
Project: Fundamental

OZR191: The application of computeralgebra within the fundamental research in geometry and theory of groups.
1/01/98 → 31/12/98
Project: Fundamental
Research output

Quantum flag manifolds as quotients of degenerate quantized universal enveloping algebras
De Commer, K. & Neshveyev, S., 2015, In : Transform. Groups. 20, 3, p. 725742 17 p.Research output: Contribution to journal › Article
2 Citations (Scopus) 
Cartesian closeness, extensionality and bornological universes
Sioen, M. & Vroegrijk, T., 2014, In : Appl. Categ. Struct.. 22, p. 565577 13 p.Research output: Contribution to journal › Article

Complexity Analysis via Approach Spaces
Colebunders, E., De Wachter, S. & Schellekens, M., Feb 2014, In : Applied Categorical Structures. 22, DOI 10.1007/s1048501393022, p. 119136 18 p.Research output: Contribution to journal › Article

Fixed points of contractive maps on DCPO's
Colebunders, E., De Wachter, S. & Lowen, B., Feb 2014, In : Mathematical Structures in Computer Science. 24, DOI:10.1017/S0960129513000017, p. 240102 18 p.Research output: Contribution to journal › Article
Open Access5 Citations (Scopus) 
Function spaces and contractive extensions in approach theory, the role of regularity
Colebunders, E., Minard, F. & Trott, W., 2014, In : Applied Categorical Structures. 22, DOI 10.1007/s104850139321z, p. 551563 13 p.Research output: Contribution to journal › Article
Activities

Workshop on Category theory
Eva Colebunders (Speaker)2012Activity: Talk or presentation › Talk or presentation at a workshop/seminar

Research visit Tholen, York University, Canada
Eva Colebunders (Member)2012Activity: Other › Types of External academic engagement  Hosting an academic visitor

Praktische toepassingen van elementaire lineaire algebra.
Rudger Kieboom (Participant)14 Feb 2012Activity: Participating in or organising an event › Participating in or organizing a public lecture/debate

Visit to the University College Cork, department CEOL.
Sarah De Wachter (Member)11 May 2011 → 28 May 2011Activity: Other › Research and Teaching at External Organisation

Bernhard Banaschewski
Eva Colebunders (Member)2011Activity: Hosting a visitor › Hosting an academic visitor