Title: Shelling the m=1 amplituhedron

 

Abstract: The amplituhedron is a topological space related to the totally nonnegative Grassmannian that was inspired by high energy physics. In this talk we will apply combinatorics and poset topology to analyze a special case known as the m=1 amplituhedron. There is a poset of sign vectors which is the closure poset of the m=1 amplituhedron, and we show this poset has an EL shelling. This implies the m=1 amplituhedron is a ball. We also show this poset is strongly Sperner.