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SUMMARY:Heat kernels in graphs: A journey from random walks to geometry\, 
 and back - He Sun\, University of Bristol
DTSTART:20150612T130000Z
DTEND:20150612T140000Z
UID:TALK59763@talks.cam.ac.uk
CONTACT:Jonathan Hayman
DESCRIPTION:Heat kernels are one of the most fundamental concepts in physi
 cs and\nmathematics. In physics\, the heat kernel is a fundamental solutio
 n of \nthe heat equation and connects the Laplacian operator to the rate o
 f \nheat dissipation. In spectral geometry\, many fundamental techniques a
 re \nbased on heat kernels. In finite Markov chain theory\, heat kernels \
 ncorrespond to continuous-time random walks and constitute one of the \nmo
 st powerful techniques in estimating the mixing time.\n\nIn this talk\, we
  will briefly discuss this line of research and its\nrelation to heat kern
 els in graphs. In particular\, we will see how heat\nkernels can be used t
 o design the first nearly-linear time algorithm for\nfinding clusters in r
 eal-world graphs. Some interesting open questions \nwill be addressed as w
 ell.\n\nThis is based on the joint work with Richard Peng (MIT)\, and Luca
  \nZanetti (University of Bristol). Parts of the results of this talk are 
 \nto appear in COLT 2015.\n
LOCATION:FW26
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