Decidability aspects of computing spectral measures
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 Lukasz Grabowski (Imperial)
 Friday 18 May 2012, 15:0016:00
 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 nontrivial?” 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 CWcomplexes known as l2Betti numbers, and how the decidability aspects related to the Atiyah conjecture on l2Betti numbers.
This talk is part of the Junior Algebra and Number Theory seminar series.
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