Published Articles & Preprints
2025
- (Book Chapter, to appear in: The Computer Algebra System OSCAR - Algorithms and Examples, book link) Gröbner Bases for Polynomial Ideals and Applications, joint with Christian Eder and Mohab Safey El Din.
2024
- (Article, ISSAC ‘24 proceedings, 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.
Preprints
-
(Article, arxiv) Wronski Pairs of Honeycomb Curves, joint with Laura Casabella and Michael Joswig.
-
(Article, arxiv) A Syzygial Method for Equidimensional Decomposition.
-
(Article, arxiv) A New Algorithm for Whitney Stratification of Varieties, joint with Martin Helmer.
Other Scientific Works
2024
- (PhD Thesis, PDF), Gröbner Basis Algorithms in Service of Algebraic Set Decomposition.
2020
- (Diploma Thesis, PDF) 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 implementation of signature-based Gröbner basis algorithms and an implementation of one of my equidimensional decomposition algorithms based on that.
- (Website) Oscar, a computer algebra system written in Julia.