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.
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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Network
Profiles

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

Kenny De Commer
 Vrije Universiteit Brussel
 Algebra and Analysis
 Mathematics  Undefined, Academic
 MathematicsTW  Academic, Undefined
 Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Professor

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

Mark Sioen
 Vrije Universiteit Brussel
 Algebra and Analysis
 Mathematics  Academic
 Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Professor

Gert Sonck
 Vrije Universiteit Brussel
 Algebra and Analysis
 Mathematics  Academic
 Studiebegeleidingscentrum  Head of Department
 Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Professor, Administrative/technical staff
Projects
 7 Finished

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


CONI537: Ischrijvingen studenten (20152016 en 20162017): voorbereiding Wiskunde voor exacte wetenschappen
1/01/16 → 31/12/17
Project: Fundamental

CONI538: Inschrijvingen studenten (20152016 en 20162017): voorbereiding Wiskunde voor humane wetenschappen
1/01/16 → 31/12/17
Project: Fundamental

CONI536: Inschrijvingen studenten (20152016 en 20162017) : Klaar voor de start
1/01/16 → 31/12/17
Project: Fundamental
Research output

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

An isomorphism of the Wallman and CechStone compactifications
Sioen, M., Colebunders, E. & Lowen, R., 2021, (Accepted/In press) In: Quaestiones Mathematicae. 31 p., https://doi.org/10.2989/16073606.2021.1891991.Research output: Contribution to journal › Article › peerreview

Frame theoretic methods in topology and analysis
Van Den Haute, W., 2021Research output: Thesis › PhD Thesis

Quantum SL(2,R)
De Commer, K., 2021, Oberwolfach report no. 44/2021: Quantum Groups – Algebra, Analysis and Category Theory. European Mathematical Society Publishing House, p. 1012 3 p. (Oberwolfach reports).Research output: Chapter in Book/Report/Conference proceeding › Meeting abstract (Book)
Open Access 
The Banaschewski compactification is of WallmanShanin type
Sioen, M. & Colebunders, E., 3 Jul 2021, In: Quaestiones Mathematicae. 44, 7, p. 905921 17 p.Research output: Contribution to journal › Article › peerreview
1 Citation (Scopus)
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)
20 Nov 2020Activity: Talk or presentation › Talk or presentation at a workshop/seminar

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

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

Quantum symmetric spaces and quantizations of semisimple real Lie groups
Kenny De Commer (Speaker)
15 Apr 2019Activity: Talk or presentation › Talk or presentation at a workshop/seminar