Projects
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 ...
Empirical Foundations for Logical Geometry: A Database of Aristotelian Diagrams KU Leuven
An intertwined study of coding theory and projective geometry. Ghent University
I investigate the intertwined properties of coding theory and projective geometry over finite fields, to obtain new results in these areas. Special attention is devoted to (q+t,t)-arcs of type (0,2,t), compressed sensing based on finite geometries, and random network coding.
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.
Non-archimedean geometry, motivic integration and rational points KU Leuven
The aim is to further investigate non-archimedean geometry, motivic integration and rational points via hensel minimality, existential positive motivic integration and quasi-analytic functions. Hensel minimality provides a geometric framework for non-archimedean geometry. Within this framework, we can study quasi-analytic functions, similar to o-minimality. This then leads to the counting and bounding of rational points. Motivic integration ...
BITSHARE: Bitstring Semantics for Human and Artificial Reasoning KU Leuven
Analytic combinatorics of the transfinite: A Tauberian approach Ghent University
This project deals with analytical methods for attacking a number of combinatorial problems arising from logic. The goal is to develop systematic tools for deriving asymptotic formulas for counting functions of proof-theoretic ordinals with the aid of Tauberian theorems for the Laplace transform. We intend to apply such formulas to extend the current knowledge on phase transitions for Gödel incompleteness results.
Nonstandard analysis in special models Ghent University
On the one hand, topology in spaces that are not first countable requires a saturated version of nonstandard analysis. On the other hand, some topological properties whose definition mentions a countable number of sets require a different version of nonstandard analysis.
The current project aims to develop a theory in which both can be combined simultaneously.
Gauging the strength of Fraisse's order-type conjecture Ghent University
We seek to find the exact logical strength of a certain mathematical theorem commonly known as Fraisse's Conjecture, using the method of Reverse Mathematics. The usual pattern in mathematics is that, in order to establish that a theorem is true, we must obtain a proof. The proof will consist of a few self-evident statements called "axioms," from which we logically deduce new statements, and so on, until eventually we arrive at the theorem in ...