Projects
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 ...
Singularities in semitoric and Poisson geometry. University of Antwerp
Geometry on groups KU Leuven
In this project, we want to study the relation between geometry and groups, both in the continuous and in the discrete setting. In the first part, we want to study geometric structures on nilpotent and solvable Lie groups, for example the existence of metrics with negative curvature or the existence of automorphisms with interesting dynamical properties. The second part puts a metric on a finitely generated group and studies how the algebraic ...
An algebraic geometry perspective on conditional independence models. Ghent University
The proposed research is at the interface of statistics and algebraic geometry. I will develop combinatorial, and geometric tools to study various statistical models from an algebraic viewpoint. In particular, I will focus on the study of Conditional Independence Models, Graphical Models, and
Gaussoids. I will use the developed techniques to study related applications in computer vision and rigidity theory.
The differential geometry of nonholonomic mechanical systems University of Antwerp
Geometry on groups KU Leuven
Applied Algebraic Geometry Ghent University
Algebraic Geometry is a branch of pure mathematics that deals with systems of polynomial equations and their solutions, which are called varieties. It has been extensively developed in the mathematical community, especially since the 20th century, e.g. by works of Grothendieck and Hilbert. What makes Algebraic Geometry special is that it connects many fields of mathematics, given that polynomials occur in many problems in various domains. ...
Toward a Unified Account of Aristotelian Diagrams in Logical Geometry. KU Leuven
Aristotelian diagrams have been widely used throughout the history of philosophy and logic, and nowadays they also have many applications in other disciplines. The framework of logical geometry studies these diagrams as objects of independent interest, which allows us to address many of the issues that surround the existing applications of these diagrams, and even to develop completely new applications. The main goal of my research program is ...
Applications of finite geometry to spectral graph theory, subspace codes and Hilbert spaces Ghent University
The proposed project consists of three topics that are linked by finite geometry. WP1 focuses on determining the cospectrality of graphs coming from finite geometries. WP2 investigates bounds on the parameters of sets of projective subspaces, with applications in Random Network Coding. WP3 translates existing quantum error correcting codes into geometrical structures to make these codes more efficient.