Projects
Derived categories and Hochschild cohomology in (noncommutative) algebraic geometry. University of Antwerp
Singularities in algebraic geometry KU Leuven
This project is in the field of algebraic geometry and is about singularities on geometrical shapes given by algebraic equations, also called algebraic varieties. We will study the effect of the presence of singularities on the geometry, the algebra, and the topology of algebraic varieties. On the geometric side, we will study contact loci of arcs associated with singularities. We aim to provide connections between contact loci and the ...
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.
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. ...
Non-commutative algebraic geometry Hasselt University
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 ...
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 ...
Topology, birational geometry and vanishing theorem for complex algebraic varieties KU Leuven
In this proposal, we focus on three aspects of algebraic varieties. Firstly, we want to study two algebro-geometric properties of smooth algebraic varieties: the linearity of the set of holomorphic 1-forms with zeros on smooth complex projective varieties, which reflects deep topological and birational nature of algebraic varieties; the surjectivity of quasi-Albanese map for smooth quasiprojective varieties, which is a crucial property for ...
Topics in singularity theory and algebraic geometry KU Leuven
We will work on selected topics in singularity theory and algebraic geometry. We will focus on uncovering the geometric details of the contact loci of polynomials inside jet spaces. There are two possible directions for applications. One is in arithmetic, where contact loci play a prominent role in the monodromy conjecture. Another one is in symplectic geometry, where contact loci are conjectured to provide an algebraic formulation of the ...