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 and Singular. This allows computing many examples in very short time for developing and checking conjectures.
Ext and Tor on two-dimensional cyclic quotient singularities (2016, to be found on the arXiv)
Thesis: Ext on affine toric varieties (published 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)