Homepage of Lars Kastner

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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: Strasse des 17. Juni 136, Room 626
e-mail: kastner[at]domain
where domain = math[dot]tu[minus]berlin[dot]de

On this website you can find my

• About me
• Curriculum vitae
• Publications
  • Papers
  • Software

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.

Furthermore I am a developer of

• mptopcom,
• OSCAR, and
• polymake.

I love clean code and TDD. I have been part of and organized several workshops and refactoring sprints.

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

• Tropical compactification via Ganter's algorithm, with Kris Shaw and Anna-Lena Winz (2020, arXiv preprint)
• Hyperplane arrangements in polymake, with Marta Panizzut (2020, arXiv, appeared in proceedings of the ICMS 2020)
• The Newton polytope of the discriminant of a quaternary cubic form, with Robert Löwe (2019, arXiv, appeared in Le Matematiche)
• Random growth on a Ramanujan graph, with Janko Boehm, Michael Joswig, and Andrew Newman (2019, arXiv preprint)
• Immaculate line bundles on toric varieties, with Klaus Altmann, Jarosław Buczyński, and Anna-Lena Winz (2018, arXiv, appeared in PAMQ)
• New counts for the number of triangulations of cyclic polytopes, with Michael Joswig (2018, In: Davenport J., Kauers M., Labahn G., Urban J. (eds) Mathematical Software – ICMS 2018. ICMS 2018. Lecture Notes in Computer Science, vol 10931. Springer, Cham, also on the arXiv)
• Parallel Enumeration of Triangulations, with Charles Jordan and Michael Joswig (2018, The Electronic Journal of Combinatorics, Volume 25, Issue 3, also on the arXiv)
• Cellular sheaf cohomology in Polymake, with Kris Shaw and Anna-Lena Winz (2017, Combinatorial Algebraic Geometry. Fields Institute Communications, vol 80. Springer, New York, NY, also on the arXiv)
• Ext and Tor on two-dimensional cyclic quotient singularities (2016, to be found on the arXiv)
• Thesis: Ext on affine toric varieties (2016, available online at Freie Universität)
• A Web Application for Macaulay2, with Franziska Hinkelmann and Michael Stillman (2015, to be found online at github)
• Negative deformations of toric singularities that are smooth in codimension two, with Klaus Altmann (2013, appeared in Deformations of surface singularities, Bolyai Mathematical Society, to be found on the arXiv)
• Calculating Generators of Multigraded Algebras, with Nathan Ilten (2013, appeared in Journal of Symbolic Computation, to be found on the arXiv)

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.
• 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.