BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Decidability aspects of computing spectral measures - Lukasz Grabo
 wski (Imperial)
DTSTART:20120518T140000Z
DTEND:20120518T150000Z
UID:TALK38054@talks.cam.ac.uk
CONTACT:Jonathan Nelson
DESCRIPTION: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 algorith
 m 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 pro
 of why there is no such algorithm for the group H^4\, where H is the lampl
 ighter group Z_2 \\wr Z. I will also explain what's the relation between c
 omputing kernels of such convolution operators and certain invariants of C
 W-complexes known as l2-Betti numbers\, and how the decidability aspects r
 elated to the Atiyah conjecture on l2-Betti numbers.
LOCATION:MR13
END:VEVENT
END:VCALENDAR