Problem of the Week
BUGCAT
Zassenhaus Conference
Hilton Memorial Lecture
BingAWM
Math Club
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.