Projects
A Kazhdan-Lusztig theorem for quantum symmetric spaces Vrije Universiteit Brussel
compact type. This conjecture is still open at the moment, although some progress has been made (in the formal case). With this project, I want ...
Projective representations of compact quantum groups and quantizations of non-compact Lie groups Vrije Universiteit Brussel
Generalized Askey-Wilson and q-Onsager algebras: a quantum algebraic approach to multivariate orthogonal polynomials. Ghent University
The central objects of this proposal are the Askey-Wilson and q-Onsager algebra. These q-deformed algebras arise as symmetry algebras of superintegrable quantum systems. We will study two generalizations, which appear when extending the systems to multiple particles, and which are algebraically derived from quantum symmetric pairs. Moreover, this allows to extend known connections with orthogonal polynomials to several variables.
Generalized Askey-Wilson and q-Onsager algebras: a quantum algebraic approach to multivariate orthogonal polynomials Ghent University
The Askey-Wilson algebra was introduced as the algebraic structure behind the Askey-Wilson orthogonal polynomials. It is closely related to the q-Onsager algebra, which originates from statistical mechanics. Both algebras appear in the context of superintegrable quantum systems. Such systems are governed by a Hamiltonian which possesses a sufficient number of symmetry operators. These symmetries are invaluable tools to solve the equations of ...
New Geometry of Quantum Dynamics (QUANTUM DYNAMICS) Vrije Universiteit Brussel
The micromechanics of DNA KU Leuven
The central focus of this thesis is the study of the physical properties of DNA, the carrier of all genetic information. These properties set the ground rules for the organization of the chromosomal genome and its interactions with the cellular machinery. In particular, the work in this thesis can be condensed into three principal aspects of DNA: Firstly, the micromechanical elasticity and its pervasive character of determining long-range ...
Beyond Classical Cosmology with the No-Boundary Wave Function KU Leuven
The goal of quantum cosmology is to find a quantum state that describes the entire evolution of our universe: from the fuzzy quantum dynamics dominating the universe’s evolution at early times to the classical cosmological evolution in our spacetime neighbourhood. Classical cosmology emerges in quantum cosmology under certain conditions only. In recent years significant progress has been made to understand the “classical realm” predicted by ...
European Integrated Research Training Network on Advanced Cryptographic Technologies for the Internet of Things and the Cloud. KU Leuven
Summary
The goal of this ETN is to develop advanced cryptographic techniques for the Internet of Things and the Cloud and to create implementations that offer a high level of security and increased usability, for a wide range of physical computation platforms. The ITN will equip a group of 15 early stage researchers with a set of interdisciplinary skills combining mathematics, computer science and electrical engineering that will ...
Duality, Geometry and Spacetime Vrije Universiteit Brussel
on a circle of large radius R and those on small ...