Colloquium : Mélissa SHERMAN-BENNETT (UC DAVIES)

Résumé :

Scattering amplitudes are functions of substantial interest to high-energy physics. They record the probability that certain particles will interact and « scatter » in a particular way. I’ll discuss the amplituhedron, a geometric object introduced by Arkan​i-Hamed and Trnka to encode scattering amplitudes. Examples of amplituhedra include cyclic polytopes, bounded chambers of cyclic hyperplane arrangements, and the totally nonnegative Grassmannian. Of particular interest from the physics perspective are decompositions of amplituhedra called « tilings », roughly analogous to subdivisions of a polytope. I’ll discuss work on tilings of the m=2 amplituhedron (with Parisi and Williams) and the m=4 amplituhedron (with Even-Zohar, Lakrec, Parisi, Tessler and Williams). The work on m=2 reveals rich combinatorics and a surprising connection to the hypersimplex. The work on m=4 resolves one of the initial conjectures of Arkani-Hamed and Trnka relating tilings to scattering amplitudes, and also connects tilings to the cluster algebra structure on the Grassmannian.