Spectra of groups generated by finite automata and the Atiyah Cojecture on L^2-Betti numbers

Rostislav Grigorchuk

Texas A & M

November 14,
refreshments at 3:45pm


We will start with a definition of a group generated by a finite automaton. A few interesting examples will be given including torsion groups of intermediate growth, Basilica group and the lamplighter group.

Then we will focus on the last example and describe the spectrum of discrete Laplace operator on Cayley grap of this group. The information about spectrum will be used to solve one question of M.Atiayh on range of L^2-Betti numbers.

We do not assume any knowledge of the L^-cohomology. The talk should be accessible to a general audience.

Speaker's Contact Info: grigorch(at-sign)math.tamu.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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