Projects
The Structure of Graph Product Operator Algebras KU Leuven
Being part of Voiculescu's groundbreaking non-commutative probability theory, free products of operator algebras are ubiquitous in the theory of operator algebras. They can be viewed as a natural operator-algebraic analogue to free products of groups where both constructions are in a certain sense compatible with each other. In the group setting free products can be generalized in terms of Green's graph products of groups. Inspired by this, ...
Quantum symmetries and operator algebras KU Leuven
Theory of operator algebras grew out of attempts at providing a useful framework for quantum mechanics. While it has served its purpose, many connections to other fields of mathematics, such as ergodic theory, have been revealed, and from then on operator algebras lived their own life, not necessarily depending on the physical motivations.
Just like classical physics turned out to be insufficient for describing the world we live in, ...
Logic, stability and perturbation theory: novel bridges between the foundations of mathematics and operator algebras KU Leuven
As all other sciences rely on mathematics, I think of science as a building, with the ground floor being made up by mathematics. As we want to keep the building in good shape so it can grow in a creative, new and strong way, we need to take care of the foundations. Logic represents these foundations. It provides the framework for mathematics (consisting of the assumptions we work with) and general abstract tools for considering mathematical ...
Construction of symmetry algebra realizations using Dirac operators Ghent University
The main aim is to construct new concrete realizations of the Lie superalgebra osp(1|2n) using Dirac operators, in the framework of Clifford analysis. These realizations will subsequently be studied from a function theoretical point of view. In particular, we wish to construct generalized integral transforms that intertwine the generators of the superalgebra. Also the connection with transvector algebras will be investigated.
Construction of symmetry algebra realizations using Dirac operators. University of Antwerp
Dual pairs and Dirac cohomology for deformations of Weyl algebras Ghent University
The goals of this project are to determine novel algebraic structures, classify their representations and study the connection with Dirac cohomology.
By studying the symmetries of deformations of the Dirac operator interesting algebraic structures arise, which do not appear in the undeformed setting. More specifically, we work inside a deformation of the Weyl algebra of linear differential operators with polynomial coefficients, ...
Axial algebras Ghent University
Non-associative algebras play an important role in many areas of mathematics. The most prominent examples are Lie algebras, introduced in the 1930s to study infinitesimal transformations. Other classes of non-associative algebras also proved vary fruitful in other areas; Jordan algebas, for instance, played a crucial role in Zel'manov's solution to the restricted Burnside problem in group theory. The goal of the proposed project is to explore ...
Braided quantum groups, actions and von Neumann algebras Vrije Universiteit Brussel
Rigidity and structural results in von Neumann algebras and Ergodic Theory KU Leuven
In their pioneering work, Murray and von Neumann found a natural way to associate a von Neumann algebra to every countable group G and to any of its measure preserving actions. The classification of these von Neumann algebras is in general a hard problem and it is driven by the following fundamental question: what aspects of the group G and of an action of G are remembered by the associated von Neumann algebras? In the amenable case, no ...