Projects
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.
Classification, symmetries and singularities at the frontiers of algebra, analysis and geometry. KU Leuven
The main goal of this Methusalem research program is to bring together KU Leuven's leading researchers in pure mathematics to focus on some of the most challenging problems in algebra, analysis, and geometry, and their numerous interactions.This Methusalem research program has the following main goals:
- Algebraic geometry. The goal is to uncover geometric properties of solution sets of algebraic equations. Combining different ...
Matroids in Applied and Combinatorial Commutative Algebra Ghent University
There is a strong interplay between combinatorics and algebraic geometry that has recently led to significant advances in both disciplines. This project focuses on the development of combinatorial and computational tools in the study of algebraic varieties, and applying these techniques to questions about matroids. It aims to (i) develop new tools using divisor theory and toric degenerations for attacking two long-standing and extremely ...
Multidegrees at the crossroads of Algebra, Geometry and Combinatorics. KU Leuven
My project is in the area of Commutative Algebra and its interactions with Algebraic Geometry, Combinatorics, and Convex Geometry. More precisely, the main goal is to study several (algebraic, geometrical and combinatorial) features of the notion of multidegrees or mixed multiplicities. The concept of multidegree provides the right generalization of degree to a multiprojective setting, and its study goes back to seminal work by van der ...
Multidegrees at the crossroads of Algebra, Geometry and Combinatorics. Ghent University
My project is in the area of Commutative Algebra and its interactions with Algebraic Geometry, Combinatorics, and Convex Geometry. More precisely, the main goal is to study several (algebraic, geometrical and combinatorial) features of the notion of multidegrees or mixed multiplicities. The concept of multidegree provides the right generalization of degree to a multiprojective setting, and its study goes back to seminal work by van der ...
Matroids in Applied and Combinatorial Commutative Algebra KU Leuven
There is a strong interplay between combinatorics and algebraic geometry, which has recently led to significant advances in both disciplines. This project focuses on the development of combinatorial and computational methods in the study of algebraic varieties, and their application to questions about matroids. The aim is (i) to develop new tools using divisor theory and toric degeneracy to address two critically important open problems in ...
Quantum symmetric spaces, operator algebras and quantum cluster algebras Vrije Universiteit Brussel
Modular representation theory of the periplectic Brauer algebra. Ghent University
Representation theory of the symmetric group can be related to representation theory of the general linear group via Schur-Weyl duality.
Similarly, Schur-Weyl duality also relates the orthogonal Lie group, the symplectic Lie group and the encompassing orthosymplectic Lie supergroup to the Brauer algebra, and it relates the periplectic Lie supergroup to the periplectic Brauer algebra.
The goal of the project is to develop modular ...