|Date: Friday, February 19, 2016
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Sign variation, the Grassmannian, and total positivity
Abstract: The totally nonnegative Grassmannian is the set of k-dimensional subspaces of R^n whose nonzero Pluecker coordinates all have the same sign. Gantmakher and Krein (1950) showed that a k-dimensional subspace is totally nonnegative if and only if every vector in it, when viewed as a sequence of n numbers and ignoring any zeros, changes sign at most k-1 times. I will present a generalization of this result, which characterizes when the vectors in a subspace change sign at most m times in terms of sign changes of certain sequences of Plucker coordinates. I will also discuss an application to the problem of defining amplituhedra and Grassmann polytopes, in the sense of Arkani-Hamed and Trnka (2013) and Lam (2015).
Speaker: Steven Karp
Institution: UC Berkeley