Title: Sign variation and boundary measurement in projective space

Date: 04/04/2019

Time: 3:00 PM - 4:00 PM

Place: C204A Wells Hall

We are interested in the topology of some spaces obtained by relaxing total positivity in the real Grassmannian. We define two families of subsets of the Grassmannian each of which include both the totally nonnegative Grassmannian and the whole Grassmannian. In this initial study of such subsets of the Grassmannian we focus of subsets of real projective space where interesting topology already appears. We we are able to find a regular CW complex which can be leveraged to compute some invariants like the fundamental group and Euler characteristic. We also conjecture some "ball-like" properties (e.g. Cohen-Macualayness).