The amplituhedron and cluster algebras

Abstract: The amplituhedron is the image of the positive Grassmannian under a linear map induced by a totally positive matrix. Special cases of the amplituhedron include the positive Grassmannian, cyclic polytopes in projective space, and the bounded complex of the cyclic hyperplane arrangement.

While at first glance the amplituhedron seems complicated, it has many beautiful properties. I will explain how ideas from oriented matroids, total positivity, and cluster algebras leads to new results about the amplituhedron.

Based on joint work with Matteo Parisi and Melissa Sherman-Bennett.

mathematical physicscommutative algebraalgebraic geometrycombinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Online Cluster Algebra Seminar (OCAS)