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SUMMARY:Total positivity is a quantum phenomenon: the grassmannian case - 
 Stephane Launois (Kent)
DTSTART:20191120T163000Z
DTEND:20191120T173000Z
UID:TALK132022@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:A real matrix is totally nonnegative if all its minors are\nno
 nnegative. This class of matrices has been studied in the past hundred\nye
 ars\, and has connection with combinatorics\, probability\, etc. This noti
 on\nof total positivity was generalised by Lusztig in the 1990s to arbitra
 ry\nflag varieties. In particular\, this led to the notion of totally nonn
 egative\ngrassmannian. In 2006\, Postnikov obtained groundbreaking results
  about a\ncell decomposition of the totally nonnegative grassmannians. In 
 particular\,\nhe described various combinatorial objects parametrising thi
 s cell\ndecomposition. Interestingly\, this cell decomposition and the ass
 ociated\ncombinatorial objects have recently found key applications in Int
 egrable\nsystems (work of Kodama-Williams on the KP equation)\, and in The
 oretical\nPhysics (work of Arkani-Hamed and coauthors on scattering amplit
 udes).\n\nIn joint work with Goodearl and Lenagan\, we showed that the cel
 l\ndecomposition of the space of totally nonnegative matrices is related t
 o a\nstratification of the prime spectrum of the algebra of quantum matric
 es. In\nthis talk\, I will review the above results and discuss the case o
 f the\n(quantum) grassmannians. This is joint work with Lenagan and Nolan.
 \n
LOCATION:MR12
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