Toric degenerations of Grassmannians: plabic graphs and tropical geometry
Abstract: Toric degenerations are a popular topic in algebraic geometry.
The basic idea is to deform any given projective variety to a toric
variety. This is desirable as toric varieties are particularly nice
given the rich combinatorics that encode many of their algebraic and
geometric properties. In this talk I will present a general result on
how to relate toric degenerations of a projective variety constructed
using a valuation to the tropicalization of this projective variety. The
leading example will be the Grassmannian and a valuation constructed by
Rietsch and Williams using Postnikov's plabic graphs and the cluster
structure on Grassmannians. The results can be found in my thesis
(https://arxiv.org/abs/1806.02090) and are partially based on joint work
with X.Fang, G.Fourier, M.Hering and M.Lanini
(https://arxiv.org/abs/1612.03838).