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 order-theoretic 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 semi-abelian categories and tensor categories Semi-abelian categories allow a unified setting for many important homological properties of non-abelian categories. Categories of quantum groups, of rings, of Lie-algebras and of crossed modules are typical non-abelian categories, often with a tensor structure. Abstract tensor categories lead to interesting non-commutative 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 semi-simple 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
- semi-simple Lie group
- Shape Theory
- Completion Theory
Fingerprint
Network
Profiles
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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
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Kenny De Commer
- Vrije Universiteit Brussel
- Algebra and Analysis
- Mathematics - Undefined, Academic
- Mathematics-TW - Academic, Undefined
- Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Professor
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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
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Mark Sioen
- Vrije Universiteit Brussel
- Algebra and Analysis
- Mathematics - Academic
- Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Professor
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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
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OZR3284: Bilateral cooperation within the framework of a joint doctoral project: Bench Fee for Joint PhD VUB-UAntwerpen, Van Den Haute Wouter
24/01/18 → 31/12/22
Project: Fundamental
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CONI537: Ischrijvingen studenten (2015-2016 en 2016-2017): voorbereiding Wiskunde voor exacte wetenschappen
1/01/16 → 31/12/17
Project: Fundamental
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CONI538: Inschrijvingen studenten (2015-2016 en 2016-2017): voorbereiding Wiskunde voor humane wetenschappen
1/01/16 → 31/12/17
Project: Fundamental
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CONI536: Inschrijvingen studenten (2015-2016 en 2016-2017) : Klaar voor de start
1/01/16 → 31/12/17
Project: Fundamental
Research output
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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 › peer-review
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An isomorphism of the Wallman and Cech-Stone 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 › peer-review
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Frame theoretic methods in topology and analysis
Van Den Haute, W., 2021Research output: Thesis › PhD Thesis
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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. 10-12 3 p. (Oberwolfach reports).Research output: Chapter in Book/Report/Conference proceeding › Meeting abstract (Book)
Open Access -
The Banaschewski compactification is of Wallman-Shanin type
Sioen, M. & Colebunders, E., 3 Jul 2021, In: Quaestiones Mathematicae. 44, 7, p. 905-921 17 p.Research output: Contribution to journal › Article › peer-review
1 Citation (Scopus)
Activities
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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
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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
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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
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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
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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