Olivetti Club

Joseph FluegemannCornell University
The Amplituhedron

Tuesday, February 15, 2022 - 4:35pm
Malott 406

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.

Refreshments will be served in the lounge at 4:00 PM.