Abstract |
I will present few results concerning spectral theory of graphs and
groups that are based on the use of multidimensional rational maps and
self-similar groups and concept of joint spectrum of a tuple of
operators. At the beginning there will be a short survey on spectra of
infinite graphs and groups. Then I will continue with some results
belonging to the speaker and his collaborators (L.Bartholdi, A.Dudko,
D.Lenz, T.Nagnibeda, V.Nekrashevych, B.Simanek and Z.Sunic) that are
based on the use of self-similar groups. The relation to the random
Schrödinger operator will be mentioned at the end of the talk.
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