Grassmann Polytopes

The amplituhedron is an object introduced by physicists in 2013 arising from their study of scattering amplitudes which has garnered much recent attention from physicists and mathematicians alike. Mathematically, it is a linear projection of a nonnegative Grassmannian to a smaller Grassmannian, via a map induced by a totally positive matrix. A Grassmann polytope, or Grasstope, is a generalization of the amplituhedron, defined to be such a projection by any matrix, removing one of the positivity conditions. In this talk, I will discuss joint work with Dmitrii Pavlov and Lizzie Pratt in which we study these objects, with hope that we may gain new insights by broadening our horizons and studying all Grasstopes.

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Date published: Wednesday, September 13, 2023