A combinatorial model for higher tropical Grassmannians

Tropical Grassmannians Trop Gr(k,n) were introduced by Speyer and Sturmfels, and in the case of 2-planes, the tropical Grassmannian can be identified with the space of phylogenetic trees. Besides the applications to mathematical biology, in recent years the tropical Grassmannian has seen new connections to scattering amplitudes in physics.

Despite its importance, the construction of a combinatorial model for higher tropical Grassmannians has remained an open problem for many years. In this work, we propose such a combinatorial model, and discuss connections with tropical linear spaces, buildings, webs, noncrossing tableaux, and matroid decompositions.

This is based on joint work with Nick Early.