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
email: kastner[at]domain
where domain = math[dot]tu[minus]berlin[dot]de
github: lkastner
On this website you can find my
Here is a picture of me.
Research interests
My main research interest lies 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 Tvarieties, i.e. varieties with an action by a lower dimensional torus.
A major part of my work involves developing and implementing algorithms for the problems I encounter. I mainly
use the systems
Macaulay2,
polymake,
Singular and
TOPCOM.
Curriculum vitae
Full CV as PDF
Publications
Papers

Tropical compactification via Ganter's algorithm, with Kristin Shaw and AnnaLena
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 AnnaLena
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 Kristin Shaw and AnnaLena
Winz
(2017, Combinatorial
Algebraic Geometry. Fields Institute Communications, vol 80. Springer, New York, NY, also on the
arXiv)

Ext and Tor on twodimensional 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
My github username is lkastner. I have contributed to the following software projects:

cellularSheaves
This is a polymake extension
for working with cellular sheaves (a special form of graph
representations), developed together with Kristin
Shaw and AnnaLena 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 GertMarting Greuel and Gerhard Pfister. I am a coauthor of the
library multigrading.lib for computations involving multigraded rings.