Homepage of Lars Kastner

• About me
• Curriculum vitae
• Publications
• Talks

codeberg github arxiv orcid

I am a postdoc at the Institute of Mathematics of the Technical University in Berlin. I am a member of the discrete geometry group of Michael Joswig.

Office: Einsteinufer 17, E-N 057
e-mail: [email protected]

About me

I am making computer experiments from mathematics and related areas FAIR. This involves developing guidelines for such computer experiments and establishing new data formats.

My mathematical interests lie at the intersection of Combinatorics with Algebraic Geometry and Commutative algebra. I wrote my thesis in the area of toric geometry and commutative algebra. Furthermore I like tropical geometry and T-varieties, i.e. varieties with an action by a lower dimensional torus.

Curriculum vitae

• 04/2022 -- present: Employee of MaRDI working on confirmable workflows
• 01/2021 -- 03/2022: Research assistant at TU Berlin, department of Mathematics
• 03/2017 -- 12/2020: Employee of the DFG transregional collaborative research centre (SFB-TRR) 195 ``Symbolic Tools in Mathematics and their Application'' at TU Berlin
• 01/2017 -- 02/2017: Employee of the DFG Priority Program SPP 1489 at FU Berlin
• 07/2016 -- 12/2016: Fields Postdoctoral Fellow at the Fields Institute in Toronto, Canada
• 2011 -- 06/2016: Employee of the DFG Priority Program SPP 1489 at FU Berlin
• 2009 -- 2010: Employee of the CRC 647 (Collaborative research center ``Space time matter'') at FU Berlin

Publications

• Papers
• Datasets
• Preprints etc
• Software

Papers

1. Casabella, Joswig, K. Subdivisions of hypersimplices: with a view toward finite metric spaces (2025) 10.1080/10586458.2024.2418831
2. K, Shaw, Winz. Tropical compactification via Ganter's algorithm (2025) 10.1007/s00454-023-00581-2
3. K. Regular Flips in mptopcom (2024) 10.1007/978-3-031-64529-7_33
4. K, Tabelow. Oh yes -- research data management (2024) 10.1515/dmvm-2024-0031
5. Boege et al. Research-data management planning in the German mathematical community (2023) 10.4171/MAG/152
6. Altmann, Buczyński, K, Winz. Immaculate line bundles on toric varieties (2020) 10.4310/PAMQ.2020.v16.n4.a12
7. K, Löwe. The Newton polytope of the discriminant of a quaternary cubic form (2020) 10.4418/2020.75.2.5
8. K, Panizzut. Hyperplane arrangements in polymake (2020) 10.1007/978-3-030-52200-1_23
9. Jordan, Joswig, K. Parallel enumeration of triangulations. (2018) 10.37236/7318
10. Joswig, K. New Counts for the Number of Triangulations of Cyclic Polytopes (2018) 10.1007/978-3-319-96418-8_31
11. K, Lorenz, Paffenholz, Winz. Toric geometry in polymake. (2018)
12. K. Toric Ext and Tor in polymake and Singular: the two-dimensional case and beyond (2017) 10.1007/978-3-319-70566-8_17
13. K, Shaw, Winz. Cellular Sheaf Cohomology in Polymake (2017) 10.1007/978-1-4939-7486-3_17
14. Altmann, K. Negative deformations of toric singularities that are smooth in codimension two. (2013) 10.1007/978-3-642-39131-6_1
15. Ilten, K. Calculating generators of multigraded algebras. (2013) 10.1016/j.jsc.2012.03.005

Datasets

1. Casabella, K, Vlad. Regular full triangulations of the Cayley polytope \$C(2\Delta\_3, 2\Delta\_3)\$ (2025) 10.5281/zenodo.15682604
2. Casabella, K, Vlad. Regular unimodular triangulations of the Cayley polytope \$C(2\Delta\_3, 2\Delta\_3)\$ (2025) 10.5281/zenodo.12820156
3. Casabella, Joswig, K. Rays of the secondary fan of the Hypersimplex(3,6) (2024) 10.5281/zenodo.12765284
4. Casabella, Joswig, K. Rays of the secondary fan of the Hypersimplex(2,7) (2024) 10.5281/zenodo.12764658
5. Casabella, Joswig, K. Regular triangulations of the Hypersimplex(3,6) (2024) 10.5281/zenodo.12665511
6. Jordan, Joswig, K. Regular unimodular triangulations of the 3-dilated 3-simplex (2024) 10.5281/zenodo.12664471
7. Jordan, Joswig, K. Regular full triangulations of the 3-dilated 3-simplex (2024) 10.5281/zenodo.12653922
8. Joswig, K. Regular triangulations of the Hypersimplex(2,7) (2024) 10.5281/zenodo.12685858

Preprints etc

1. Frühbis-Krüger, Joswig, K. Drawing real plane algebraic curves in OSCAR (2026) arxiv:2603.12985
2. Geiselmann et al. 121 Patchworked Curves of Degree Seven (2026) arxiv:2602.06888
3. Geiselmann et al. Fast Isotopy Computation for T-Curves (2026) arxiv:2604.09221
4. Casabella, K, Vlad. Tropical elliptic curves in 3-space (2025) arxiv:2507.21958
5. Consortium. Research Data Management Planning in Mathematics v2 (2025) 10.5281/zenodo.16678203
6. Casabella, Joswig, K. Subdivisions of Hypersimplices: with a View Toward Finite Metric Spaces (2024)
7. Casabella, Joswig, K. Supplementary scripts for computations of coarsest subdivisisions of hypersimplices (2024) 10.5281/zenodo.13881795
8. K. Scripts for parsing the output of TOPCOM and mptopcom (2024) 10.5281/zenodo.13880566
9. Boehm, Joswig, K, Newman. Random growth on a Ramanujan graph (2019)
10. K. Ext and Tor on two-dimensional cyclic quotient singularities (2016) arxiv:1601.05673
11. K. Ext on affine toric varieties (2016) 10.17169/refubium-5247

Software

• cellularSheaves This is a polymake extension for working with cellular sheaves (a special form of graph representations), developed together with Kris Shaw and Anna-Lena Winz. These sheaves can be used for computing tropical homology. You can find more information here and here.
• Macaulay2 Computer algebra system developed by Michael Stillman and Daniel Grayson. I am currently one of the maintainers of the ‘Polyhedra’ package for computations involving polyhedral objects.
• mptopcom Framework for computing triangulations of point configurations using parallel environments. Based on TOPCOM. Heavily uses the polymake callable library for the new mathematical parts. Parallelization is done by mts. The algorithms are described in the article Parallel Enumeration of Triangulations.
• OSCAR Next generation computer algebra system based on polymake, Singular, GAP and (written in) Julia.
• polymake Software framework for computations involving polyhedral objects. Together with Benjamin Lorenz I am author of the application ideal for interfacing Singular, as well as of the application fulton for toric geometry.
• Singular Computer algebra system developed by Gert-Marting Greuel and Gerhard Pfister. I am a co-author of the library multigrading.lib for computations involving multigraded rings.

Talks

• Slides for my talk at the Computer Algebra, Number Theory and More conference in Leipzig.