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 Algebraic Geometry Ghent University
Algebraic Geometry is a branch of pure mathematics that deals with systems of polynomial equations and their solutions, which are called varieties. It has been extensively developed in the mathematical community, especially since the 20th century, e.g. by works of Grothendieck and Hilbert. What makes Algebraic Geometry special is that it connects many fields of mathematics, given that polynomials occur in many problems in various domains. ...
The present project proposes a research path focussed on multisymplectic geometry and on its applications to modern physics. Just as symplectic geometry is the natural arena for the classical mechanics of point-like systems, multisymplectic geometry encompasses field theories as well, thus providing a powerful and unifying finite dimensional portrait suitable for the description of a rich variety of physical systems. Symplectic geometry ...
Symplectic geometry is the mathematical framework which was created to most efficiently describe classical mechanics. It dates back to Hamilton's formulation of Newton's laws of motion, in the 1800s. The modern subject, however, was truly born much more recently, in the 1960s and 1970s, following the discovery of surprising "rigid" and "flexible" phenomena. The subject has become a study in the tension between these two conflicting ...
In the previous years, I have studied various techniques from algebraic combinatorics and their
possible applications to Galois geometry. Algebraic techniques such as eigenvalue methods, linear
programming, clique-coclique bounds, and rank arguments turned out to be very successful in
tackling open problems in finite geometry (upper bounds on subspace codes, EKR theorems). This
is not a one-way street. Galois ...
Subgraphs and codes in distance-regular graphs in incidence geometry Ghent University
My project includes the application of techniques in algebraic graph theory, to obtain new bounds and non-existence results in geometry. Conversely, finite geometries can yield new (distance-regular) graphs with certain properties, and algebraic techniques can yield a characterization of them. In particular, I intend to further examine a proposed construction relying on substructures in a specific dual polar graph.
Derived categories and Hochschild cohomology in (noncommutative) algebraic geometry. University of Antwerp
Symplectic Techniques in Differential Geometry. University of Antwerp
The Geometry of Singular Foliations KU Leuven
Foliation theory is a classical subject within differential geometry, since the work of Reeb in the 1950s. It studies how a given space can be decomposed smoothly into subspaces of smaller dimension, called leaves. We study decompositions in which the dimension of the leaves can vary, as for the decomposition of 3-dimensional Euclidean space into concentric spheres about the origin, together with the origin. Rather than studying the ...
The geometry of MRD codes Ghent University
The proposal focuses on the relation between finite geometry and coding theory. Our attention
goes specifically to maximum rank distance codes or MRD codes. These are a particular type of
rank codes, which describe a systematic way of building codes that could detect and correct
multiple random rank errors.
The aim of this research is to get a deeper understanding of the geometry behind MRD codes, and