====== Benjamin Schroeter (Binghamton) ======

====== Shortest Paths and Tropical Geometry ======

===== Abstract for the Combinatorics Seminar 2019 February 19 =====

One of the most basic classes of algorithmic problems in combinatorial optimization is the computation of shortest paths. Tropical geometry is a natural language to analyze parametrized versions where some of the arc weights are unknown. I will introduce this point of view, with a link to polyhedral geometry. Moreover, I will present two applications for those graphs, traffic networks and the enumeration of polytropes, building blocks of tropical convexity. This is ongoing work with Michael Joswig.


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