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Unwinding The Amplituhedron

Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017

October 12, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Hugh Thomas (Université du Québec à Montréal)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

Arkani-Hamed and Trnka recently defined an object, which they dubbed the amplituhedron, which encodes the scattering amplitudes for planar N=4 super Yang-Mills.  This object feels polytopal, and indeed, in simple examples, it is a cyclic polytope inside projective space.  However, in general, it lives in a Grassmannian rather than in a projective space.  Amplituhedra are closely linked to the geometry of total positivity; indeed, the totally non-negative part of a Grassmannian is also an example of an amplituhedron.  I will try to explain some of what this means, and report on joint work with Arkani-Hamed and Trnka in which we give a new and simpler definition of the amplituhedron

Supplements
29714?type=thumb Hugh Notes 2.08 MB application/pdf Download
29715?type=thumb Hugh Notes 2.08 MB application/pdf Download
Video/Audio Files

13-Thomas

H.264 Video 13-Thomas.mp4 413 MB video/mp4 rtsp://videos.msri.org/data/000/029/601/original/13-Thomas.mp4 Download
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