Described by Quanta Magazine as "A Jewel at the Heart of Quantum Physics," the Amplituhedron has been an active topic of research for both mathematicians and physicists in the last 5-10 years.
Building on the work of Grassmannian scattering amplitudes in arXiv:1212.5605, where terms in computations of quantum field theoretic scattering amplitudes correspond to the positroid varieties studied by Allen Knutson and his collaborators, Arkani-Hamed and Trnka in arXiv:1312.2007 found that these amplitudes could be considered as the volume of a geometric object which is a projection of a positive Grassmannian called the Amplituhedron. These terms will be defined in the talk.
I plan to start by giving the mathematical definition of the Amplituhedron, and briefly survey some of the results obtained primarily by Harvard's Lauren Williams and her collaborators described in arXiv:2110.10856. I then plan on describing some of the motivation for why people care about this object coming from physics (but still very mathematical). I may describe the Associahedron as an example of the Amplituhedron for a particular quantum field theory.