Georg Loho, London School of Economics and Political Science

PDL C401
Convexity for the maxplus algebra has been studied from different directions including discrete geometry, scheduling, computational complexity. As there is no inverse for the maxoperation, this used to rely on an implicit nonnegativity 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 compare it with the discrete structure of classical polytopes and thereby highlight the differences with convexity over the signed tropical numbers. We finish with an overview of several natural formulations in terms of balance relations, polytopes over Puiseux series and hyperoperations.