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# Orders and polytropes: matrices from valuations

## January 21, 2022 at 14:00 – 15:00 CET

TGiZ-Seminar: Tropical geometry in Zoom (First meeting Winter Semester 2021/22)

14:00-15:00 Mima Stanojkovski (RWTH Aachen)

Abstract:

Let K be a discretely valued field with ring of integers R. To a d-by-d matrix M with integral coefficients one can associate an R-module, in K^{d x d}, and a polytope, in the Euclidean space of dimension d-1. We will look at the interplay between these two objects, from the point of view of tropical geometry and building on work of Plesken and Zassenhaus. This is joint work with Y. El Maazouz, M. A. Hahn, G. Nebe, and B. Sturmfels.