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 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
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Collaborations and top research areas from the last five years
Profiles
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Eva Colebunders
- Vrije Universiteit Brussel
- Mathematics & Data Science
- Mathematics - Undefined
- Vriendenkring VUB - Emeritus
- Topological Algebra, Functional Analysis and Category Theory
Person: Sympathiser, Researcher
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Tomas Everaert
- Vrije Universiteit Brussel
- Mathematics - Practice assistant
- Mathematics & Data Science - Practice assistant
- Topological Algebra, Functional Analysis and Category Theory
Person: Researcher
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Gert Sonck
- Vrije Universiteit Brussel
- Education - Service Department Director
- Mathematics
- Topological Algebra, Functional Analysis and Category Theory
Person: Researcher, Administrative/technical staff
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EUPOM141: Supporting Professionals and Academics for Community Engagement in Higher Education (SPACE)
Engels, N., Moriau, L., Sonck, G., Cocquyt, C., Mostmans, L., Hidding, K. & Komac, I.
1/11/23 → 31/10/26
Project: Applied
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FWOTM1160: Braided quantum groups, actions and von Neumann algebras
Krajczok, J. & De Commer, K.
1/10/23 → 30/09/26
Project: Fundamental
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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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Research output
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Braided tensor product of von Neumann algebras
De Commer, K. & Krajczok, J., 2024, (Submitted).Research output: Working paper › Preprint
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Generalized spectra and applications to finite distributive lattices
Sioen, M., Van Den Haute, W. & Lowen, W., 2024, In: Journal of Pure and Applied Algebra. 6, 8 p., 107588.Research output: Contribution to journal › Article › peer-review
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Invariant integrals on coideals and their Drinfeld doubles
De Commer, K. & Dzokou Talla, J. R., 1 Jul 2024, In: International Mathematics Research Notices. 2024, 14, p. 10650-10677 28 p., rnae094.Research output: Contribution to journal › Article › peer-review
1 Citation (Scopus) -
Quantum SL(2,R) and its irreducible representations
De Commer, K. & Dzokou Talla, J. R., 2024, In: Journal of Operator Theory. 91, 2, p. 443-470 28 p.Research output: Contribution to journal › Article › peer-review
Open Access2 Citations (Scopus) -
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. 1-79 79 p., e14.Research output: Contribution to journal › Article › peer-review
Open AccessFile2 Citations (Scopus)51 Downloads (Pure)
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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Aspects of Higher Representation Theory
Kenny De Commer (Chair)
21 Jan 2019 → 25 Jan 2019Activity: Participating in or organising an event › Participating in or organizing a school event
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Research visit `Fields Institute'
Kenny De Commer (Chair)
2019 → …Activity: Participating in or organising an event › Participating in or organizing an event at an external academic organisation