Projects
Bernstein-Sato polynomial and geometry of singularities KU Leuven
The theory of D-modules and Bernstein-Sato polynomials are fundamental tools to study algebraic singularities. This proposal consists of three projects to expand the understanding of this interaction. Specifically: (1) the study of the Bernstein-Sato polynomial of a locally complete intersection and its minimal exponent, (2) some open problems regarding the roots of the Bernstein-Sato polynomial of non-degenerate singularities, and (3) the ...
Questions on singularities of convolutions of polynomial maps KU Leuven
We propose to study several questions on the behavior of singularities of polynomial maps under an algebraic convolution operation.
Given a polynomial map f to an algebraic group, we consider a convolution operation which produces a new polynomial map f*f into the same group. Similarly to the usual convolution operation in analysis, outcomes f*f of the algebraic convolution operation have improved singularity properties. In this ...
Singularities in algebraic geometry KU Leuven
This project is in the field of algebraic geometry and is about singularities on geometrical shapes given by algebraic equations, also called algebraic varieties. We will study the effect of the presence of singularities on the geometry, the algebra, and the topology of algebraic varieties. On the geometric side, we will study contact loci of arcs associated with singularities. We aim to provide connections between contact loci and the ...
Classification, symmetries and singularities at the frontiers of algebra, analysis and geometry. KU Leuven
This Methusalem project is a collaboration of all research groups in pure mathematics at KU Leuven. Our research focuses on five main areas of pure mathematics: algebraic geometry, algebraic topology & group theory, classical analysis, differential geometry and functional analysis. Our goal is to make progress on some of the most challenging open problems in these areas, including the monodromy conjecture on motivic zeta functions, ...
The Singularities of Hyperplane Arrangements KU Leuven
We propose three projects exploring the frontier of the singularities of hyperplane arrangements. The proposal considers the logarithmic content of hyperplane arrangements, charting new ideas and techniques for solving classical problems involving algebraic differential operators. Specifically: (1) proving that hyperplane arrangements satisfy the Strong Monodromy Conjecture; (2) giving a differential operator (or D-module) interpretation of ...
Bernstein-Sato polynomials and Hodge ideals of Algebraic Singularities KU Leuven
In this project we plan to study the Bernstein-Sato polynomials and the Hodge ideals associated to algebraic singularities. The BernsteinSato polynomial of an algebraic singularity is a difficult invariant to study, which is related to many other invariants of the singularity. For this object, we plan to study its roots from the geometry of the singularity. In particular, for plane curve singularities we want to determine the subsets of the ...
Noncommutative crepant resolutions for three- and higher- dimensional singularities Vrije Universiteit Brussel
Within algebraic geometry ...
Non-commutative resolutions of quotient singularities for reductive groups - INCOMING [Pegasus]² Marie Sklodowska-Curie Fellowship: Appllicant Spela Spenko Vrije Universiteit Brussel
Our research proposal is about resolutions of singularities. The basic idea is to replace a singular space with a nonsingular one ...
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 ...