Projects
The arithmetic of Campana curves KU Leuven
The study of Diophantine problems - finding rational or integral solutions to (systems) of polynomial equations - dates back more than 2000 years, and yet still drives some of the most prominent developments in arithmetic geometry. The quest for a better understanding of rational and integral points on algebraic varieties is challenging, not in the least for one-dimensional varieties, and has led to a number of well-known highlights such as ...
The Shape of blame: investigating the gradual nature of judgments of blame and praise through the mathematical estimation of ‘blame-praise curves’. Ghent University
For “gradual behaviours”, whether a specific instance of that behaviour is blame- or praiseworthy depends on how much of the behaviour is done. For instance, for a behaviour like “replying quickly to emails”, whether a specific reply is blame or praiseworthy will depend on the timeliness of that reply. Such behaviours lie on a continuum in which part of the continuum is praiseworthy (replying quickly) and another part of the continuum is ...
Berkovich curves, semistable reduction and wild ramification KU Leuven
Around 1990, Vladimir Berkovich constructed powerful foundations for analytic geometry over non-archimedean fields, such as p-adic fields and fields of Laurent series. This theory has found a broad range of applications in number theory, algebraic geometry and dynamical systems. The aim of the project is to construct generalizations of Michael Temkin's work on norms on pluricanonical forms and its applications to wildly ramified covers of ...
Berkovich Skeleta and Wildly Ramified Curves KU Leuven
In mathematics, the field of arithmetic geometry is essentially the study of arithmetic problems like solving equations over the rational numbers using methods inspired from geometry. An equation like x²+y²=1 defines a curve in the plane, in this case a circle, and finding rational solutions of this equation, like (x,y)=(3/5,4/5), is the same as finding special points on this circle, the so-called rational points. Finding rational points on ...
Curves as covers of the projective line KU Leuven
Most of current public-key cryptography is considered insecure against attacks from sufficiently powerful quantum computers. Post-quantum cryptography studies methods to secure information resistant against such attacks. One proposal is isogeny-based cryptography, which bases its security on computational hardness assumptions related to maps between elliptic curves. We analyze the security of isogeny-based cryptographic schemes, in particular ...
Inference after model selection and averaging via confidence distributions and curves KU Leuven
Model selection and model averaging are common practices to find the best model that explains the observed data. When the working model is selected using data-driven methods and the same data are used for inference about population parameters, guarantees of classical inference techniques might not hold anymore. This dissertation discusses ways of producing valid inference for post-selection and for model averaged estimators via confidence ...
Diameter-height curves for domains managed by the Agency for Nature and Forest (EVINBO) Research Institute for Nature and Forest
The statistical behavior of Frobenius in families of curves over finite fields KU Leuven
My PhD is about syzygies of toric varieties and curves on toric surfaces.
Toric geometry is a part of algebraic geometry of a very combinatorial flavour, where to each lattice polygon or polytope one can associate a projective variety.
syzygies is about graded free resolutions of a projective variety, whose structure is summarized in the graded Betti table, which is a table of integers.
I try to find (and prove) links ...
Linear systems on curves and graphs. KU Leuven
Research consists primarily of studying the specialization of theta characteristics on hyperelliptic curves and graphs by using lifts of harmonic morphisms and the specialization image.