Homepage of Lars Kastner

LK

Lars Kastner

I am a postdoc at the Institute of Mathematics of the Technical University in Berlin.

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

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 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.

Papers

Immaculate line bundles on toric varieties, with Klaus Altmann, Jarosław Buczyński, and Anna-Lena Winz (2018, arXiv preprint)
Parallel Enumeration of Triangulations, with Charles Jordan and Michael Joswig (2018, The Electronic Journal of Combinatorics, Volume 25, Issue 3, 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

My github username is   lkastner.
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.