Combinatorics of the Tree Amplituhedron
Geometric and topological combinatorics: Modern techniques and methods October 09, 2017  October 13, 2017
Location: SLMath: Eisenbud Auditorium
amplituhedron
total positivity
plane partitions
Naryana number
12Williams
The tree amplituhedron A(n, k, m) is a geometric object generalizing the positive Grassmannian, which was introduced by ArkaniHamed andTrnka in 2013 in order to give a geometric basis for the computationof scattering amplitudes in N = 4 supersymmetric YangMills 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 nonintersecting lattice paths and plane partitions.
This is joint work with Steven Karp, and part of it is additionally joint work with Yan Zhang
Williams Notes

Download 
12Williams
H.264 Video 
12Williams.mp4

Download 
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.