BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Melissa Sherman-Bennett (UC Berkeley) DTSTART:20210715T163000Z DTEND:20210715T173000Z DTSTAMP:20260422T054403Z UID:SFUQNTAG/34 DESCRIPTION:Title: The hypersimplex and the m=2 amplituhedron: Eulerian numbers\, sign flip s\, triangulations\nby Melissa Sherman-Bennett (UC Berkeley) as part o f SFU NT-AG seminar\n\n\nAbstract\nPhysicists Arkhani-Hamed and Trnka intr oduced the amplituhedron to better understand scattering amplitudes in N=4 super Yang-Mills theory. The amplituhedron is the image of the totally no nnegative Grassmannian under the "amplituhedron map"\, which is induced by matrix multiplication. Examples of amplituhedra include cyclic polytopes\ , the totally nonnegative Grassmannian itself\, and cyclic hyperplane arra ngements. In general\, the amplituhedron is not a polytope. However\, Luko wski--Parisi--Williams noticed a mysterious connection between the m=2 amp lituhedron and the hypersimplex\, and conjectured a correspondence between their fine positroidal subdivisions. I'll discuss joint work with Matteo Parisi and Lauren Williams\, in which we prove one direction of this corre spondence. Along the way\, we prove an intrinsic description of the m=2 am plituhedron conjectured by Arkhani-Hamed--Thomas--Trnka\; give a decomposi tion of the m=2 amplituhedron into Eulerian number-many sign chambers\, in direct analogy to a triangulation of the hypersimplex\; and find new clus ter varieties in the Grassmannian.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/34/ END:VEVENT END:VCALENDAR