Projects
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. ...
Applications of finite geometry in spectral graph theory and in classical and quantum error-correction Ghent University
The proposed project consists of three topics that are linked by finite geometry and by the techniques that are used to investigate them. They are situated in modern research areas with many applications and are of current international interest. We devote a work package (WP) to each topic. WP1 (Finite geometry and spectral graph theory) focuses on determining the cospectrality of graphs coming from finite geometries, thus giving new insights ...
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 ...
On Submanifolds and Deformations in Poisson Geometry KU Leuven
This thesis concerns specific classes of submanifolds in Poisson geometry. The emphasis lies on normal form statements, and we present an application in
deformation theory. The results are divided into three themes.
We first study coisotropic submanifolds in log-symplectic manifolds. We provide a normal form around coisotropic submanifolds transverse to the degeneracy locus, and we prove a reduction statement for coisotropic ...
Towards a Systematic Theory of Aristotelian Diagrams in Logical Geometry KU Leuven
Aristotelian diagrams, such as the square of opposition, have been widely used throughout the history of philosophy and logic. Nowadays, they also have several applications in other disciplines that are concerned with logical reasoning, such as psychology, linguistics and computer science. However, many of the applications of Aristotelian diagrams suffer from substantial problems, often due to a lack of understanding of the intricate logical ...
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 ...
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 ...
Duality, Geometry and Spacetime Vrije Universiteit Brussel
on a circle of large radius R and those on small ...
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 ...