Yelena Mandelshtam | Combinatorics of m=1 Grasstopes

Amplituhedra, Cluster Algebras, and Positive Geometry Conference
May 29, 2024
Speaker: Yelena Mandelshtam, UC Berkeley
Title: Combinatorics of m=1 Grasstopes
Abstract: A Grasstope is a linear projection of the totally nonnegative Grassmannian to a smaller Grassmannian. This is a generalization of the amplituhedron, a geometric object of great importance to calculating scattering amplitudes in physics. The amplituhedron is a Grasstope arising from a totally positive linear map. While amplituhedra are relatively well-studied, much less is known about general Grasstopes. In this talk, I will discuss combinatorics and geometry of Grasstopes in the m=1 case. In particular, I will show that they can be characterized as unions of cells of a hyperplane arrangement satisfying a certain sign variation condition and argue that amplituhedra are (in a certain sense) minimal Grasstopes. This is based on joint work with Dmitrii Pavlov and Lizzie Pratt.