Decidability aspects of computing spectral measures

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• Lukasz Grabowski (Imperial)
• Friday 18 May 2012, 15:00-16:00
• MR13.

If you have a question about this talk, please contact Jonathan Nelson.

CANCELLED

Given a finitely generated group G we can fix a generating set g_1, g_2, ... g_n and consider T to be a random walk (or more general convolution operator) on the Cayley graph of G wrt the generators g_1, ..., g_n. In the talk we will investigate computational problems related to computing the spectral measure of T: in particular, is there an algorithm which answers the question “is the kernel of T non-trivial?” I will give many examples of groups where there is such an algorithm and sketch a proof why there is no such algorithm for the group H^4, where H is the lamplighter group Z_2 \wr Z. I will also explain what’s the relation between computing kernels of such convolution operators and certain invariants of CW-complexes known as l2-Betti numbers, and how the decidability aspects related to the Atiyah conjecture on l2-Betti numbers.

This talk is part of the Junior Algebra and Number Theory seminar series.

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