Presented By: Student Combinatorics Seminar - Department of Mathematics
The Twist for Positroid Varieties, Part 2
Yucong Lei
Last week we introduced positroid varieties and their descriptions through bounded affine permutations and equivalently Grassmann necklaces, and talked about some relevant plabic graph combinatorics. In this talk, we pick up from the boundary measurement map to give a parametrization of points in the positroid. We will then introduce the twist automorphism, which will connect the image of the boundary measurement map to the nonvanishing information given by face labels of a plabic graph. We will then give a combinatorial way of computing twisted face pluckers from "minimal matchings" of the plabic graph, which will turn out to be invertible, hence showing the boundary measurement map is an open inclusion into the positroid variety over complex numbers.