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SUMMARY:Towards a calculus for nonlinear spectral gaps - Assaf Naor (Coura
 nt/Weizmann)
DTSTART:20090306T163000Z
DTEND:20090306T173000Z
UID:TALK16281@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:The spectral gap of a symmetric stochastic matrix is the\nreci
 procal of the best constant in its associated Poincare inequality. This\ni
 nequality can be formulated in purely metric terms\, where the metric is a
 \nHilbertian metric. This immediately allows one to define the spectral ga
 p of\na matrix with respect to other\, non-Euclidean\, geometries: a stand
 ard\nprocedure which is used a lot in embedding theory\, most strikingly a
 s a\nmethod to prove non-embeddability in the coarse category. Motivated b
 y a\ncombinatorial approach to the construction of bounded degree graph fa
 milies\nwhich do not admit a coarse embedding into any uniformly convex no
 rmed space\n(such spaces were first constructed by Lafforgue)\, we will na
 turally arrive\nat questions related to the behavior of non-linear spectra
 l gaps under graph\noperations such as powering and zig-zag products. We w
 ill also discuss the\nissue of constructing base graphs for these iterativ
 e constructions\, which\nleads to new analytic and geometric challenges.
LOCATION:MR4\, CMS
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