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Title:
Spectral analysis on self-similar graphs and fractals
Speaker:
Abstract:
The talk will describe how spectral theory, geometry of graphs, and dynamical systems are used to analyze spectral properties of the random walk generator on finitely ramified self-similar graphs and fractals. In particular, pure point or singular continuous spectrum appears naturally for such graphs. The standard examples include the Sierpinski triangle, the Vicsek tree, and the Schreier graphs of the Hanoi self-similar group studied by Grigorchuk and Sunic. A more complicated example is related to the Basilica Julia set of the polynomial z^2-1 and its Iterated Monodromy Group, defined by Nekrashevych. Its spectrum was investigated numerically by Strichartz et al and analytically in a joint work with Luke Rogers and several students at UConn.
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