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SUMMARY:Lauren Williams (Harvard)
DTSTART:20200921T190000Z
DTEND:20200921T200000Z
DTSTAMP:20260423T021446Z
UID:WHCGP/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WHCGP/17/">H
 ow is the hypersimplex related to the amplituhedron?</a>\nby Lauren Willia
 ms (Harvard) as part of Western Hemisphere colloquium on geometry and phys
 ics\n\n\nAbstract\nIn 1987\, Gelfand-Goresky-MacPherson-Serganova made a b
 eautiful\nconnection between the geometry of the Grassmannian and convex p
 olytopes\, via\nthe moment map\; the moment map image of the Grassmannian 
 Gr(k\,n) is a polytope\nknown as the hypersimplex Delta(k\,n).  In 2013\, 
 motivated by the desire to\ngive a geometric basis for the computation of 
 scattering amplitudes in N=4\nSYM\, Arkani-Hamed and Trnka introduced the 
 amplituhedron A(n\,k\,m) as the image\nof the positive Grassmannian Gr+(k\
 ,n) under a linear map Z from R^n to R^{k+m}\nwhich is totally positive.  
 While the case m=4 is most relevant to physics\,\nthe amplituhedron makes 
 sense for any m.  In my talk I will explain some\nstrange parallels betwee
 n the positroidal subdivisions of the hypersimplex\nDelta(k+1\,n) and the 
 m=2 amplituhedron A(n\,k\,2).  One link is provided by the\npositive tropi
 cal Grassmannian.  Attributions: based on joint works with Tomek\nLukowski
 \, Matteo Parisi\, and David Speyer.\n\nDisclaimer: I'm neither a geometer
  nor a physicist.\n
LOCATION:https://researchseminars.org/talk/WHCGP/17/
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