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SUMMARY:Random planar curves and conformal invariance - Wendelin Werner (U
 niversité Paris-Sud)
DTSTART:20010710T170000Z
DTEND:20010710T180000Z
UID:TALK24058@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Understanding the behaviour of certain natural very long rando
 m curves in the plane is a seemingly simple question that has turned out t
 o raise deep questions\, some of which remain unsolved. \nFor instance\, t
 heoretical physicists have predicted (and this is still an open problem) t
 hat the number a(N) of self-avoiding curves of length N on the square latt
 ice Z × Z grows asymptotically like C^{N} N^{11/32} for some constant C. 
 More generally\, theoretical physicists (Nienhuis\, Cardy\, Duplantier\, S
 aleur etc.) have made predictions concerning the existence and values of c
 ritical exponents for various two-dimensional systems in statistical physi
 cs (such as self-avoiding walks\, critical percolation\, intersections of 
 simple random walk) using considerations related to several branches of ma
 thematics (probability theory\, complex variables\, representation theory 
 of infinite-dimensional Lie algebras). \nWe give a general introduction to
  the subject and briefly present some recent mathematical progress\, inclu
 ding work of Kenyon\, Werner\, Smirnov\, Lawler\, and Schramm.\n
LOCATION:Wolfson Hall\, Churchill College\, Cambridge
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