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Isaac Newton Institute for Mathematical Sciences

Self-similar groups and Schur complement.

13th June 2007

Author: Rostislav Grigorchuk (Texas A&M)

Abstract

The talk will contain a discussion of the technique based on the matrix transfomation known as Schur complement. It enables one to compute in certain situations the spectra of discrete Laplace operators on self-similar groups and associated Schreier graphs (which usually inherit the self-similar structure), and of elements in associated C*- algebras. This technique will be applied to show usefullnes of Schur complement in study of random walks on groups and in proving amenability. KNS spectral measures will be mentioned and for a torsion group of intermediate growth a result will be formulated about the relation between this measure and Kesten spectral measure. This relation will be used to compute Jacobi parameters of the corresponding Markov operator.