Projects
Categorification and quantisation of cluster type structures Vrije Universiteit Brussel
governed by symmetries. Representation theory seeks for
symmetries, in order to shed light on the observed objects, and also
to collect them into abstract entities, which aid to distinguish and
compare different objects. The main type of entities investigated in
this project are those modelled by a Lie algebra, whose prominent
role in ...
Matroids in Applied and Combinatorial Commutative Algebra Ghent University
There is a strong interplay between combinatorics and algebraic geometry that has recently led to significant advances in both disciplines. This project focuses on the development of combinatorial and computational tools in the study of algebraic varieties, and applying these techniques to questions about matroids. It aims to (i) develop new tools using divisor theory and toric degenerations for attacking two long-standing and extremely ...
Exploiting combinatorial structures for algebraic and geometric decompositions Ghent University
We will develop novel tools to solve several important real-world problems: (i) Proving safety of programs (Computer Science), (ii)
Computing network reliability (Industrial Engineering), (iii) Causality (Statistics), and (iv) Geometry of particle interactions (Physics).
These problems are all traditionally modeled as polynomial systems. However, given that solving a general system is very difficult, they all lack scalable ...
Stacks and duality in non-commutative algebraic geometry. University of Antwerp
Stacks and duality in non-commutative algebraic geometry. University of Antwerp
The Amplituhedron: Algebra, Combinatorics, and Positive Geometry KU Leuven
The proposed project lies within the field of algebraic geometry and its interconnections with combinatorics, polyhedral geometry, mathematical physics, and real algebraic geometry. The central focus of the project is the study of the amplituhedron, a novel geometric object at the intersection of mathematics and physics. This research is motivated by the finding of explicit formulas for computing scattering amplitudes, which are the ...