(Article, preprint, arxiv) Computing Generic Fibers of Polynomial
Ideals Using FGLM and Hensel Lifting, joint with Jérémy Berthomieu.
2023
(Article, ISSAC ‘23 proceedings, arxiv) A Direttissimo Algorithm
for Equidimensional Decomposition, joint with Christian Eder,
Pierre Lairez and Mohab Safey El Din.
2022
(Article, Journal of Symbolic Computation, arxiv) A Signature-based
Algorithm for Computing the Nondegenerate Locus of a Polynomial
System, joint with Christian Eder, Pierre Lairez and Mohab Safey El
Din.
Articles In Preparation
On a new algorithm for Whitney stratifications, joint with Martin Helmer.
On an algorithm for decomposing algebraic sets using signature Gröbner bases.
Gröbner Bases for Polynomial Ideals and Applications, chapter in the upcoming Oscar book,
joint with Christian Eder and Mohab Safey El Din.
Other Scientific Works
2020
(Diploma thesis) In my diploma thesis I used Picard-Lefschetz theory
to compute the periods of a projective hypersurface. It was
supervised by Emre Sertöz during his stay at the MPIMiS in Leipzig
and Bernd Sturmfels.
Software
(GitHub) AlgebraicSolving.jl, a Julia package for polynomial system
solving. I contributed an improved version of the F5 algorithm
mentioned below.
(Website) Oscar, a computer algebra system written in Julia.
(GitHub) Julia implementation of the F5 algorithm and the
Algorithm presented in the Nondegenerate Locus paper.