Grasstopes

The amplituhedron is an object defined by physicists to understand particle scattering, and has garnered much recent attention from physicists and mathematicians alike. Mathematically, it is a linear projection of a positive Grassmannian to a smaller Grassmannian, via a totally positive matrix. Generalizing the amplituhedron, we define a Grasstope to be such a projection by any matrix.

In this talk we ask: can we gain new insights by broadening our horizons, and systematically studying all Grasstopes? I will explain some current work with Yelena Mandelstam and Dmitrii Pavlov in this direction.