Projects
Automorphism groups of rank 2 geometries associated to exceptional groups of Lie type Ghent University
The aim of the project is to determine the automorphism groups of prominent geometric structures—some of them are new, some of them relate to important long standing open problems). All geometries are related to Tits Buildings, introduced by Abel prize recipient Jacques Tits in the 60s of last century, and thus have a strong link with algebraic structures, in particular with simple algebraic groups, or, more generally, groups of Lie type. The ...
Exploiting combinatorial structures for algebraic and geometric decompositions. KU Leuven
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 algorithms. The ...
Reestablishing smoothness for matrix manifold optimization via resolution of singularities. KU Leuven
OZR backup mandate: Skew braces, quivers, and applications to the Yang-Baxter equation. Vrije Universiteit Brussel
The first one is to study the structure theory of skew braces. The project is to deal with the classification of skew braces of prime- power size. The plan is to start analysing those of size a power of 2. Then developing group-theoretical techniques ...
Solutions of the Yang-Baxter equation and associated algebraic structures Vrije Universiteit Brussel
This project is motivated by this open problem. In particular, we are very interested in the group and ring theoretic aspects that arise. More precisely, with ...
Dynkin-like Categories: Root Systems, Clusters, and Generalized Associahedra Ghent University
My proposal is about continuous generalizations of the connections among three concepts: root systems, cluster structures, and generalized associahedra. The three concepts, in the finite discrete setting, are partially classified by the Dynkin diagrams: An, Bn, Cn, Dn, E6, E7, E8, F4, and G2. The same diagrams classify many other objects throughout mathematics and physics. I have worked on a continuous cluster structure of type A and am ...
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 ...
Advances and applications of symmetric tensor decomposition KU Leuven
My project revolves around algebraic and numerical techniques applied to symmetric tensor decomposition. These objects have been attracting considerable attention in the last decades as they provide efficient tools for managing large amounts of data. Their decomposition is often employed for optimizing their computational use or for extracting hidden information from the considered systems.
The approach I intend to pursue is twofold. ...