Projects
Combinatorial and Computational Algebraic Geometry KU Leuven
My project lies in the area of Commutative Algebra and its interactions with Algebraic Geometry, Tropical Geometry, Combinatorics, and Convex Geometry. The main goal is to associate convex polytopes to algebraic varieties such that significant geometric properties of the variety can be read off from their polytopes. A toric variety is a certain algebraic variety modeled on a convex polytope. My main goal is to develop new and unifying tools ...
Applied and Computational Algebraic Geometry KU Leuven
This PhD proposal centers on systems of polynomial equations that mathematically model several problems in network reliability theory, rigidity theory, and statistics. The main idea is to exploit combinatorial and geometric structures in these systems and use them to efficiently study their solutions spaces. Solving systems of polynomials in general is extremely difficult, however, in the aforementioned applications, the main problem is ...
Real Algebraic Geometry: theory and computation KU Leuven
Finite Geometry, Coding Theory and Cryptography Ghent University
Coding theory and cryptography are two interacting research areas, of great relevance for our modern society. More and more information is transmitted via computers, often via wireless networks. The increase in transmitted data continuously asks for better codes and for better cryptographical techniques to ensure a correct and secure transmission of the information. Coding theory constructs codes for the transmission of information through a ...
Geometry Estimation of Twin Robot X-Ray Computed Tomography Systems KU Leuven
This thesis will focus on high accuracy control of collaborating robot systems, aiming to provide accurate positioning and orienting ability for a flexible robotic X-ray CT system. Industrial X-ray ct system has gained more and more attention because of the outstanding ability to perform quality control on both internal and external structure. However, current CT systems can only perform on fixed circular trajectories, which restrict its ...
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. ...
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 ...
Development of an integrated modelling approach to study the interaction between joint contact geometry, kinematics and loading applied to the knee KU Leuven
Studying the relation between joint geometry, kinematics and loading is essential to understand how joints function, but is even more important from a clinical perspective. Deviant kinematics may, for example, adversely affect joint loading patterns, with load concentration on specific articular regions which might increase the risk of developing osteoarthritis(OA). OA is the most common agerelated joint disorder and is characterized by ...