# Projects

## Derived categories and Hochschild cohomology in (noncommutative) algebraic geometry. University of Antwerp

## Non-commutative algebraic geometry Hasselt University

## An algebraic geometry perspective on conditional independence models. Ghent University

The proposed research is at the interface of statistics and algebraic geometry. I will develop combinatorial, and geometric tools to study various statistical models from an algebraic viewpoint. In particular, I will focus on the study of Conditional Independence Models, Graphical Models, and

Gaussoids. I will use the developed techniques to study related applications in computer vision and rigidity theory.

## Combinatorial and Computational Algebraic Geometry KU Leuven

## Topology, birational geometry and vanishing theorem for complex algebraic varieties KU Leuven

In this proposal, we focus on three aspects of algebraic varieties. Firstly, we want to study two algebro-geometric properties of smooth algebraic varieties: the linearity of the set of holomorphic 1-forms with zeros on smooth complex projective varieties, which reflects deep topological and birational nature of algebraic varieties; the surjectivity of quasi-Albanese map for smooth quasiprojective varieties, which is a crucial property for ...

## Topics in singularity theory and algebraic geometry KU Leuven

We will work on selected topics in singularity theory and algebraic geometry. We will focus on uncovering the geometric details of the contact loci of polynomials inside jet spaces. There are two possible directions for applications. One is in arithmetic, where contact loci play a prominent role in the monodromy conjecture. Another one is in symplectic geometry, where contact loci are conjectured to provide an algebraic formulation of the ...

## The dictionary between algebraic geometry and the combinatorics of graphs and polyhedra. KU Leuven

Algebraic geometry is the branch of mathematics studying sets of solutions to systems of polynomial equations, which pop up in a variety of research fields, ranging over pure mathematics, hard-core engineering (robotics), molecular biology, information technology, and theoretical physics. In studying such sets, a tool of emerging importance is the analysis of certain of their combinatorial `shadows', that typically appear in the form of ...

## 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. ...

## Algebraic Semidefinite Programming for Codes and Anti-Codes in Finite Geometry Ghent University

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 ...