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SUMMARY:The geometry and topology of random polygons - Cantarella\, J (Uni
 versity of Georgia)
DTSTART:20120920T103000Z
DTEND:20120920T113000Z
UID:TALK39943@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Here is a natural question in statistical physics: What is the
  expected shape of a polymer with n monomers in solution? The correspondin
 g mathematical question is equally interesting: Consider the space of n-go
 ns in three dimensional space with length 2\, modulo translation. This is 
 a compact manifold. What is the natural metric (and corresponding probabil
 ity measure) on this manifold? And what are the statistical properties of 
 n-gons in 3-space sampled uniformly from this probability measure?\n\nIn t
 his talk\, we describe a natural probability measure on length 2 n-gon spa
 ce pushed forward from the standard measure on the Stiefel manifold of 2-f
 rames in complex n-space. The pushforward map comes from a construction of
  Hausmann and Knutson from algebraic geometry.\n\nWe will be able to expli
 citly and exactly compute the expected value of the radius of gyration for
  polygons sampled from our measure\, and also give a fast algorithm for di
 rectly sampling the space of closed polygons.  The talk describes joint wo
 rk with Malcolm Adams (University of Georgia\, USA)\, Tetsuo Deguchi (Ocha
 nomizu University\, Japan)\, and Clay Shonkwiler (University of Georgia\, 
 USA).\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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