Projects
Orthogonal polynomials and special functions: theory and applications KU Leuven
We study special functions that appear frequently in several scientific disciplines and applications. Usually these functions
appear as a solution of a differential equation or a recursive relation. We are particularly interested in orthogonal
polynomials: these are families of polynomials that satisfy a number of orthogonality conditions that are given by integrals.
Such polynomials are used in approximation theory ...
Compression of neural networks using tensor decompositions and decoupling of multivariate polynomials KU Leuven
The problem of decoupling multivariate functions in block-oriented system identification has led to the creation of tensor methods for determining the parameters and internal representations of non-linear static components. Current methods focus on solving the initial single-layer decoupling problem. However, more complex non-linearities may require multi-layer representations. Because of this, the first aim of this project is to generalize ...
Algorithms for finding roots of multivariate polynomials with engineering applications KU Leuven
This PhD will be integrated in the research program ‘Back to the roots’ under the ERC Advanced Grant of prof. dr. Bart De Moor. This program is about sets of multivariate polynomials, optimization problems, numerical linear algebra and operator theory. The PhD topic will be on developing new insights in this framework on system identification and parameter estimation for dynamical polynomial systems in one and more dimensions.
Algorithms for finding roots of multivariate polynomials with engineering applications KU Leuven
This PhD will be part of the research funded by the ERC Advanced Research Grant ‘Back to the roots’, which provides a general framework based om multidimensional system theory, numerical linear algebra and optimization, and operator theory to come up with new algorithms for rooting sets of multivariate polynomials.
Bernstein-Sato polynomials and Hodge ideals of Algebraic Singularities KU Leuven
In this project we plan to study the Bernstein-Sato polynomials and the Hodge ideals associated to algebraic singularities. The BernsteinSato polynomial of an algebraic singularity is a difficult invariant to study, which is related to many other invariants of the singularity. For this object, we plan to study its roots from the geometry of the singularity. In particular, for plane curve singularities we want to determine the subsets of the ...
Random tilings and matrix valued orthogonal polynomials KU Leuven
The aim of this research project is to study random tilings of planar domains with very special properties.
The tiling problems we have in mind have a rich combinatorial structure which allows for explicit formulas of relevant probabilistic quantities.
The expicit formulas are in many cases tractable to asymptotic analysis when the system size tends to infinity.
In recent work a specific model called the two-periodic ...
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 ...
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.
Matrix valued orthogonal polynomials and applications KU Leuven
Matrix-valued functions are relevant and useful in situations where non-commutativity is important, i.e, when the order in which one performs certain operations plays a role. We aim to find a relation between a number of physical models and matrix-valued special functions, in, particular polynomials. Our interest is in non-commutative Toda lattices and non-commutative Painlevé equations which were recently introduced. Our knowledge on how ...