Projects
The Kneser-Tits problem for linear algebraic groups of type E_8 of relative rank 2 Ghent University
A fundamental problem in the theory of linear algebraic groups is the Kneser-Tits problem. For most groups of relative rank 2, the solution to the Kneser-Tits problem is known. The remaining groups of relative rank 2 for which the problem is unsolved, are two groups of type E_8. Both problems can be reduced to purely algebraic questions. The research in the direction of the study of these problems offers a lot of opportunities.
Computational aspects of algebraic curves and their applications. KU Leuven
Bernstein-Sato polynomials and Hodge ideals of Algebraic Singularities KU Leuven
In this project we plan to study the Bernstein-Sato polynomials and the Hodge ideals associated to algebraic singularities. The BernsteinSato polynomial of an algebraic singularity is a difficult invariant to study, which is related to many other invariants of the singularity. For this object, we plan to study its roots from the geometry of the singularity. In particular, for plane curve singularities we want to determine the subsets of the ...
Reduction theory of arithmetic surfaces and applications to quadratic forms over algebraic function fields University of Antwerp
Algebraic cycles on hyperkähler varieties. University of Antwerp
Riemann-Hilbert morphism RH(X) for a smooth complex algebraic variety KU Leuven
For a smooth complex algebraic variety X, one can define a (Betti) moduli space of complex local systems on X, M_B(X). Choosing a nice compactification with boundary a simple normal crossings divisor, one also defines a (de Rham) moduli space of logarithmic flat connections, M_DR(X). These are algebraic varieties related by an analytic morphism of their underlying complex manifolds, RH(X): M_DR(X) --> M_B(X). In the projective case, this ...