Lecture by Georg Loho (London School of Economics and Political Science): Signed tropical convexity

Nov 25, 2019 | 02:15 PM

Convexity for the max-plus algebra has been studied from different directions including discrete geometry, scheduling, computational complexity. As there is no inverse for the max-operation, this used to rely on an implicit non-negativity assumption. We remove this restriction by introducing `signed tropical convexity'. This allows to exhibit new phenomena at the interplay between computational complexity and geometry. We obtain several structural theorems including a new Farkas lemma and a Minkowski-Weyl theorem for polytopes over the signed tropical numbers. Our notion has several natural formulations in terms of balance relations, polytopes over Puiseux series and hyperoperations.

Time & Location

Nov 25, 2019 | 02:15 PM

Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin
Room 005 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)