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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The geometry and topology of random polygons - Can
tarella\, J (University of Georgia)
DTSTART;TZID=Europe/London:20120920T113000
DTEND;TZID=Europe/London:20120920T123000
UID:TALK39943AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39943
DESCRIPTION:Here is a natural question in statistical physics:
What is the expected shape of a polymer with n mo
nomers in solution? The corresponding mathematical
question is equally interesting: Consider the spa
ce of n-gons in three dimensional space with lengt
h 2\, modulo translation. This is a compact manifo
ld. What is the natural metric (and corresponding
probability measure) on this manifold? And what ar
e the statistical properties of n-gons in 3-space
sampled uniformly from this probability measure?\n
\nIn this talk\, we describe a natural probability
measure on length 2 n-gon space pushed forward fr
om the standard measure on the Stiefel manifold of
2-frames in complex n-space. The pushforward map
comes from a construction of Hausmann and Knutson
from algebraic geometry.\n\nWe will be able to exp
licitly and exactly compute the expected value of
the radius of gyration for polygons sampled from o
ur measure\, and also give a fast algorithm for di
rectly sampling the space of closed polygons. The
talk describes joint work with Malcolm Adams (Uni
versity of Georgia\, USA)\, Tetsuo Deguchi (Ochano
mizu University\, Japan)\, and Clay Shonkwiler (Un
iversity of Georgia\, USA).\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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