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SUMMARY:A random walk around soluble group theory - Peter Kropholler (Univ
 ersity of Southampton)
DTSTART:20170512T133000Z
DTEND:20170512T143000Z
UID:TALK72496@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Karl Lorensen		(Penn State Altoona)\, Armand
 o Martino		(Southampton)\, Conchita Martinez Perez		(Zaragoza)\, Lison Jac
 oboni		(Orsay)        <br></span><br>This talk is about new developments i
 n the theory of soluble (aka solvable) groups. In the nineteen sixties\, s
 eventies\, and eighties\, the theory of infinite solvable groups developed
  quietly and unnoticed except by experts in group theory. Philip Hall&#39\
 ;s work was a major impact and inspiration but before that there had been 
 pioneering work of Maltsev and Hirsch. In the eighties\, new vigour was br
 ought to the subject through the work of Bieri and Strebel: the BNS invari
 ant was born and for the first time there appeared a connection between th
 e abstract algebra of Maltsev\, Hirsch and Hall\, and the topological and 
 geometric insights of Thurston\, Stallings and Dunwoody. <br><br>Nowadays\
 , solvable groups are vital for a number of reasons. They are a primary so
 urce of examples of amenable groups\, exhibiting a rich display of propert
 ies as shown in work of\, for example\, Erschler. There is an intimate con
 nection with 3 manifold theory: we imagine that 3 manifolds revolve around
  hyperbolic geometry. But if hyperbolic geometry is the sun at the centre 
 of the 3 manifold universe then Sol Nil S^3 S^2xR and R^3 (5 of the remain
 ing 7 geometries identified by Thurstons geometrization programme must be 
 the outlying planets: all virtually solvable and very much full of life. W
 e might think of these solvable geometries as in some way the trivial case
 s. But they have also been an inspiration both in algebra and in geometry.
  <br><span><br>In this talk I will take a survey that leads in a meanderin
 g way through solvable infinite groups and culminates in a study of random
  walks on Cayley graphs including recent work joint with Lorensen as well 
 as independent results of Jacoboni.</span>
LOCATION:Seminar Room 1\, Newton Institute
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