Projects
Manin matrices and non-communicative algebraic geometry Vrije Universiteit Brussel
Algebraic Geometry. KU Leuven
This thesis is devoted to the study of certain cases of a conjecture of Greenberg and Benois on derivative of p-adic L-functions using the method of Greenberg and Stevens. We first prove this conjecture in the case of the symmetric square of a parallel weight 2 Hilbertmodular form over a totally real field where p is inert and whose associated automorphic representation is Steinberg in p, assuming certain hypotheses on the conductor. This ...
Real Algebraic Geometry: theory and computation KU Leuven
Diophantine problems and algebraic geometry: new connections. KU Leuven
The core idea of this research proposal is that there is a lot to be gained from an intensified interaction between different subfields of arithmetic/algebraic geometry. The community of people studying rational points on algebraic varieties (to which I belong) is now very big and mature, but it would benefit enormously from more interaction with other, rapidly developing subfields of algebraic geometry, such as birational and logarithmic ...
Diophantine equations and algebraic geometry: new connections KU Leuven
Algebraic and Geometric Properties of Matroids KU Leuven
Mijn project valt binnen het gebied van combinatorische algebraïsche meetkunde. Ik bestudeer algebraïsche variëteiten die zijn gedefinieerd vanuit combinatorische objecten en mijn doel is om te zien hoe meetkundige invarianten van dergelijke variëteiten kunnen worden afgeleid uit de onderliggende combinatoriek. Ik zal me richten op matroïde variëteiten; deze zijn irreducibele componenten van vele andere variëteiten. Matroïden verenigen ...
New Geometric and Algebraic Foundations of Coding Theory Ghent University
Algebraic coding theory was created in order to design error-correcting codes for reliable data transmission through noisy channels. However, coding theory is also used when there is control on the channel, and errors are designed ad-hoc for privacy/security purposes. This is the case of secret sharing schemes: a secret is shared among several participants, who can access it only if enough of them agree. In this project, I will develop a more ...
Exploiting combinatorial structures for algebraic and geometric decompositions Ghent University
We will develop novel tools to solve several important real-world problems: (i) Proving safety of programs (Computer Science), (ii)
Computing network reliability (Industrial Engineering), (iii) Causality (Statistics), and (iv) Geometry of particle interactions (Physics).
These problems are all traditionally modeled as polynomial systems. However, given that solving a general system is very difficult, they all lack scalable ...