Projects per year
Organisation 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.
Keywords
 Incidence Geometry
 Categorical Homotopy Theory
 Topological Foundation Of Quantumtheory
 Algebraic Topology
 Flag Transitive Groups
 Operator algebra
 Hyperspaces
 quantum deformation
 non commutative spaces
 Cartesian Closedness
 Convergence Theory
 Approach theory
 Categorical Topology
 Approximation theory
 semisimple Lie group
 Shape Theory
 Completion Theory
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Collaborations and top research areas from the last five years
Profiles

Eva Colebunders
 Vrije Universiteit Brussel
 Algebra and Analysis
 Mathematics  Undefined
 Vriendenkring VUB  Emeritus
 Topological Algebra, Functional Analysis and Category Theory
Person: Sympathiser, Researcher, Professor

Tomas Everaert
 Vrije Universiteit Brussel
 Algebra and Analysis
 Mathematics  Practice assistant, Temporary replacement ZAP
 Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Professor

Gert Sonck
 Vrije Universiteit Brussel
 Education  Service Department Director
 Algebra and Analysis
 Mathematics
 Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Professor, Administrative/technical staff

EUPOM141: Supporting Professionals and Academics for Community Engagement in Higher Education (SPACE)
Engels, N., Moriau, L., Sonck, G., Cocquyt, C. & Mostmans, L.
1/11/23 → 31/10/26
Project: Applied

FWOTM1160: Braided quantum groups, actions and von Neumann algebras
Krajczok, J. & De Commer, K.
1/10/23 → 30/09/26
Project: Fundamental

OZR3284: Bilateral cooperation within the framework of a joint doctoral project: Bench Fee for Joint PhD VUBUAntwerpen, Van Den Haute Wouter
24/01/18 → 31/12/22
Project: Fundamental

Research output

Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik–Zamolodchikov equations and Letzter–Kolb coideals
De Commer, K., Yamashita, M., Neshveyev, S. & Tuset, L., 2 May 2023, In: Forum of Mathematics: Pi. 11, 14, p. 179 79 p., e14.Research output: Contribution to journal › Article › peerreview
Open AccessFile16 Downloads (Pure) 
Partial ⁎algebraic quantum groups and Drinfeld doubles of partial compact quantum groups
De Commer, K. & Konings, J., Nov 2023, In: Journal of Algebra. 634, p. 345403 59 p.Research output: Contribution to journal › Article › peerreview
Open Access 
An isomorphism of the Wallman and ČechStone compactifications
Sioen, M., Colebunders, E. & Lowen, R., 4 May 2022, In: Quaestiones Mathematicae. 45, 5, p. 733763 31 p.Research output: Contribution to journal › Article › peerreview

Quantum SL(2,R) and its irreducible representations
De Commer, K. & Dzokou Talla, J. R., 2022, (Accepted/In press) In: Journal of Operator Theory.Research output: Contribution to journal › Article › peerreview

Sequences and related closure and compactness properties in frames
Sioen, M., Holgate, D. & Masuret, J., 15 Mar 2022, In: Topology and its Applications. 309, 12 p., 107912.Research output: Contribution to journal › Article › peerreview
Activities

Commissie Topsport VUB: Dual career at the Vrije Universiteit Brussel  New facts & figures
Koen De Brandt (Speaker), Paul Wylleman (Speaker), Evert Zinzen (Contributor) & Gert Sonck (Contributor)
14 Jan 2021Activity: Talk or presentation › Talk at a school event

A quantization of Sylvester's law of inertia
Kenny De Commer (Speaker)
8 Oct 2020Activity: Talk or presentation › Talk or presentation at a workshop/seminar

A quantization of Sylvester's law of inertia
Kenny De Commer (Speaker)
20 Nov 2020Activity: Talk or presentation › Talk or presentation at a workshop/seminar

Maria Manuel Clementino
Mark Sioen (Host)
31 Jan 2019 → 2 Feb 2019Activity: Hosting a visitor › Hosting an academic visitor

Quantized twisted adjoint orbits and quantum symmetric spaces
Kenny De Commer (Speaker)
13 Aug 2019Activity: Talk or presentation › Talk or presentation at a workshop/seminar