Publications and Preprints

Multi-splits and tropical linear spaces from nested matroids Multi-splits and tropical linear spaces from nested matroids [arXiv:1707.02814]
Abstract
In this paper we present an explicit combinatorial description of a special class of facets of the secondary polytopes of hypersimplices. These facets correspond to polytopal subdivisions called multi-splits. We show a relation between the cells in a multi-split of the hypersimplex and nested matroids. Moreover, we get a description of all multi-splits of a product of simplices. Additionally, we present a computational result to derive explicit lower bounds on the number of facets of secondary polytopes of hypersimplices.
Algorithms for Tight Spans and Tropical Linear Spaces Algorithms for Tight Spans and Tropical Linear Spaces [arXiv:1612.03592]
Abstract
We describe a new method for computing tropical linear spaces and more general duals of polyhedral subdivisions. It is based on Ganter's algorithm (1984) for finite closure systems.
with Simon Hampe and Michael Joswig
Matroids from hypersimplex splits Matroids from hypersimplex splits
Abstract
A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases. As their key feature these split matroids can be studied via techniques from polyhedral geometry. It turns out that the structural properties of the split matroids can be exploited to obtain new results in tropical geometry, especially on the rays of the tropical Grassmannians.
with Michael Joswig
The degree of a tropical basis The degree of a tropical basis
Abstract
We give an explicit upper bound for the degree of a tropical basis of a homogeneous polynomial ideal. As an application f-vectors of tropical varieties are discussed. Various examples illustrate differences between Gröbner and tropical bases.
with Michael Joswig
Parametric linear programs and convex hulls Parametric linear programs and convex hulls
Abstract
We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful for computations in tropical geometry.
with Michael Joswig, Georg Loho and Benjamin Lorenz

Poster and Others

Dressians and tropical Grassmannians Dressians and tropical Grassmannians [Poster for MEGA2015]
Poster Dressians and tropical Grassmannians
presented at MEGA2015
Tropical Grassmannian TropGr(2,6) Tropical Grassmannian TropGr(2,6) [Model]
The tropical Grassmannian TropGr(2,6)
interactive model for the DGD Gallery with Michael Joswig