Lars KastnerI am a postdoc at the Institute of Mathematics of the Technical University in Berlin.
Office: Strasse des 17. Juni 136, Room 626
where domain = math[dot]tu[minus]berlin[dot]de
Research interestsMy 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 T-varieties, 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. This allows computing many examples in very short time for developing and checking conjectures.
Immaculate line bundles on toric varieties, with Klaus Altmann, Jarosław Buczyński, and Anna-Lena Winz (2018, arXiv preprint)
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 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)
SoftwareMy github username is lkastner.
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.