Projects
Cohomological invariants of structurable algebras Ghent University
A common theme in algebra is to understand algebraic structures over arbitrary fields by first studying them over their algebraic closure and then investigating the possible ways to "descend" to the base field again. A typical example occurs in the theory of quadratic forms over an arbitrary field. In order to decide when two given quadratic forms are non-isometric, a useful tool is to define invariants for quadratic forms; typical (easy) ...
Differential graded algebras and their Brauer Group theory Hasselt University
Skew braces and applications Vrije Universiteit Brussel
(YBE) in algebra and beyond. Rather than working directly with solutions, we focus on skew braces, a
closely-related novel algebraic structure that has been the subject of intensive research over the last
few years. The theory of skew braces is a fertile meeting ground for group theory, ring theory,
geometry, and ...
New methods in field arithmetic and quadratic form theory. University of Antwerp
Hilbert's Tenth Problem and diophantine sets Ghent University
Hilbert's Tenth Problem is about (un)decibability of diophantine equations. One of the field we study are function fields over valued fields in characteristic 0. Under certain conditions on the valuation and the Galois cohomology we can prove undecidability. We also investigate whether diophantine sets are recursively enumerable for certain polynomial rings, for example over a number field.