Combinatorics of the tree amplituhedron

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• Lauren Williams (UC Berkeley)
• Tuesday 03 July 2018, 17:00-18:00
• CMS, MR2.

If you have a question about this talk, please contact HoD Secretary, DPMMS.

The tree amplituhedron A(n, k, m) is a geometric object generalizing the positive Grassmannian, which was introduced by Arkani-Hamed and Trnka in 2013 in order to give a geometric basis for the computation of scattering amplitudes in N=4 supersymmetric YangMills theory. I will give a gentle 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. 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.

The lecture will be followed by a wine reception in the Central Core, CMS .

This talk is part of the The LMS Hardy Lecture series.

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