Leonie Kayser

Office G3 05

Hi, I’m Leonie, a PhD student in math at MPI MiS, Leipzig. I’m a member of the Nonlinear Algebra Group, my advisor is Simon Telen. I am interested in Commutative Algebra and Algebraic Geometry with a view towards computation and applications.

I studied both mathematics and computer science at Leibniz University Hannover from 2016 to 2022. I wrote my master’s theses on The Waring problem for polynomials under Matthias Schütt and on Gröbner Bases and Their Complexity under Heribert Vollmer.

Upcoming events

Sep 6–8: Conference on Applied Algebra at Osnabrück University

Past events

Jul 10–14: SIAM Conference on Applied Algebraic Geometry (AG23) at TU Eindhoven
Jun 07–08: Let’s get ℝeal at MPI MiS, Leipzig
May 31–Jun 1: 10. Computeralgebra-Tagung der Fachgruppe at LUH, Hannover
May 22–24: Commutative Algebra TOwards Applications at Politecnico and Università di Torino
Apr 3–4: Workshop on Solving hard polynomial systems at MPI MiS, Leipzig
Mar 9: Seminar day on Algebra, Geometry and Computation at CWI, Amsterdam
Feb 9–10: Northern German Algebraic Geometry Seminar at HU Berlin
Dec 13–14, 2022: Macaulay2 Bootcamp at MPI MiS, Leipzig
Nov 28–Dec 1, 2022: Computational Geometry School at Fraunhofer ITWM, Kaiserslautern

news

Aug 1, 2023	Together with Yannik Mahlau and Lukas Berg we won an Outstanding Paper Award in the ML Reproducibility Challenge 2022! For an overview check out the Kaggle notebook!
Jul 6, 2023	My first preprint just went online! Check it out on arXiv:2307.02560.
May 24, 2023	I became a maintainer of the MathRepo! What is MathRepo?
Apr 11, 2023	I am the first face of the Math Planck People series! Check out the article here.
Jan 28, 2023	Hello world. This website just launched!

selected publications

2023

Hilbert Functions of Chopped Ideals

Fulvio Gesmundo, Leonie Kayser, and Simon Telen

Jul 2023

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A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite set of points as the original one-dimensional ideal. The complexity of computing these points from the chopped ideal is governed by the Hilbert function and regularity. We conjecture values for these invariants and prove them in many cases. We show that our conjecture is of practical relevance for symmetric tensor decomposition.
[Re] On Explainability of Graph Neural Networks via Subgraph Explorations

Yannik Mahlau, Leonie Kayser, and Lukas Berg

ReScience C, Jul 2023

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Yuan et al. claim their proposed method SubgraphX achieves (i) higher fidelity in explaining models for graph- and node classification tasks compared to other explanation techniques, namely GNNExplainer. Additionally, (ii) the computational effort of SubgraphX is at a ’reasonable level’, which is not further specified by the original authors. We define this as at most ten times slower than GNNExplainer. We reimplemented the proposed algorithm in PyTorch. Then, we replicated the experiments performed by the authors on a smaller scale due to resource constraints. Additionally, we checked the performance on a new dataset and investigated the influence of hyperparameters. Lastly, we improved SubgraphX using greedy initialization and utilizing fidelity as a score function.