Projects
From Poisson geometry to Jacobi geometry and beyond KU Leuven
Poisson geometry is an active area with many applications. It is known that Poisson, contact and lcs geometries have a common extension: Jacobi geometry. It is the geometry of Jacobi structures: Lie brackets on sections of a line bundle that are 1st order bidifferential operators (DOs). Although its feature, Jacobi geometry is far less studied than Poisson geometry. The project aims at studying Jacobi structures with tools from Poisson ...
Applied and Computational Algebraic Geometry KU Leuven
Symmetry reduction and unreduction in mechanics and geometry. University of Antwerp
Tensor products in non-commutative geometry and higher deformation theory University of Antwerp
Beyond Symplectic Geometry KU Leuven
Symplectic geometry was created as the mathematical foundation of classical mechanics. At the start of the
twentieth century it became the foundation also of quantum mechanics. And since the advent of string theory it
has played a key role in quantum field theory too. The aim of this project is to take the ideas and techniques of
symplectic geometry and apply them to new fields, not in physics, but in geometry itself. We will ...
Derived categories and Hochschild cohomology in (noncommutative) algebraic geometry. University of Antwerp
Deformation problems in Poisson and generalized complex geometry KU Leuven
In geometry, it is interesting to consider not just a specific geometric structure on a manifold, but the space of geometric structures of that type. We often consider this space modulo a natural equivalence relation. For example, we can look at symplectic structures modulo isotopies. Global statements are in many cases too much to ask for, which is why we consider small deformations of a structure, giving a description of nearby structures. ...
Classification, symmetries and singularities at the frontiers of algebra, analysis and geometry. KU Leuven
The main goal of this Methusalem research program is to bring together KU Leuven's leading researchers in pure mathematics to focus on some of the most challenging problems in algebra, analysis, and geometry, and their numerous interactions.This Methusalem research program has the following main goals:
- Algebraic geometry. The goal is to uncover geometric properties of solution sets of algebraic equations. Combining different ...
Statistical Mechanics of Geometry. KU Leuven
Curved surfaces are ubiquitous in Nature, from the microscopic level with bent cell membranes to the grand scale of cosmology, where general relativity is the ruling theory. This PhD project explores the connections between statistical physics and geometric structures (graphs, networks, surfaces and manifolds), something we call 'Statistical Mechanics of Geometry'. The main objective is to examine the effects of geometric degrees of freedom ...