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 ...
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 is 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 representation ...
Developments and applications of categorical algebra Vrije Universiteit Brussel
The objective of this proposal is twofold: to use computational and algebraic methods in order to advance in the development of categorical algebra, and to apply the existing categorical-algebraic knowledge and techniques in order to obtain novel approaches of ...
The Amplituhedron: Algebra, Combinatorics, and Positive Geometry KU Leuven
The proposed project lies within the field of algebraic geometry and its interconnections with combinatorics, polyhedral geometry, mathematical physics, and real algebraic geometry. The central focus of the project is the study of the amplituhedron, a novel geometric object at the intersection of mathematics and physics. This research is motivated by the finding of explicit formulas for computing scattering amplitudes, which are the ...