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SUMMARY:Amplituhedra\, Scattering Amplitudes and Triangulations
DESCRIPTION:Member Seminar \nSpeaker: Matteo Parisi \nTitle: Amplituhedra\, Scattering Amplitudes and Triangulations \nAbstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular\, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes\, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known\, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory\, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts\, such as matroid theory\, torus orbits in the Grassmannian\, and tropical geometry. Based on joint works with Lauren Williams\, Melissa Sherman-Bennett\, Tomasz Lukowski [arXiv:2104.08254\, arXiv:2002.06164].
URL:https://cmsa.fas.harvard.edu/event/2-11-2022-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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