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Combinatorics of the Tree Amplituhedron

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

October 12, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Lauren Williams (Harvard University)
Location: MSRI: Simons Auditorium
  • amplituhedron

  • total positivity

  • plane partitions

  • Naryana number

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



The tree amplituhedron A(n, k, m) is a geometric object generalizing the positive Grassmannian, which was introduced by Arkani-Hamed andTrnka in 2013 in order to give a geometric basis for the computationof scattering amplitudes in N = 4 supersymmetric Yang-Mills theory. Iwill give an elementary introduction to the amplituhedron, and then describe what it looks like in various special cases. For example, one can use the theory of sign variation and matroids to show that the amplituhedron A(n, k, 1) can be identified with the complex of bounded faces of a cyclic hyperplane arrangement (and hence is homeomorphic to a closed ball). I will also present some conjectures relating the amplituhedron A(n, k, m) to combinatorial objects such as non-intersecting lattice paths and plane partitions.

This is joint work with Steven Karp, and part of it is additionally joint work with Yan Zhang



29713?type=thumb Williams Notes 3.09 MB application/pdf Download
Video/Audio Files


H.264 Video 12-Williams.mp4 92.6 MB video/mp4 rtsp://videos.msri.org/data/000/029/599/original/12-Williams.mp4 Download
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