BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A random walk around soluble group theory - Peter
Kropholler (University of Southampton)
DTSTART;TZID=Europe/London:20170512T143000
DTEND;TZID=Europe/London:20170512T153000
UID:TALK72496AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72496
DESCRIPTION:Co-authors: Karl Lorensen (Penn State Altoo
na)\, Armando Martino (Southampton)\, Conchita Ma
rtinez Perez (Zaragoza)\, Lison Jacoboni (Orsay)
This talk is about new deve
lopments in the theory of soluble (aka solvable) g
roups. In the nineteen sixties\, seventies\, and e
ighties\, the theory of infinite solvable groups d
eveloped quietly and unnoticed except by experts i
n group theory. Philip Hall'\;s work was a majo
r impact and inspiration but before that there had
been pioneering work of Maltsev and Hirsch. In th
e eighties\, new vigour was brought to the subject
through the work of Bieri and Strebel: the BNS in
variant was born and for the first time there appe
ared a connection between the abstract algebra of
Maltsev\, Hirsch and Hall\, and the topological an
d geometric insights of Thurston\, Stallings and D
unwoody.
Nowadays\, solvable groups are vi
tal for a number of reasons. They are a primary so
urce of examples of amenable groups\, exhibiting a
rich display of properties as shown in work of\,
for example\, Erschler. There is an intimate conne
ction with 3 manifold theory: we imagine that 3 ma
nifolds revolve around hyperbolic geometry. But if
hyperbolic geometry is the sun at the centre of t
he 3 manifold universe then Sol Nil S^3 S^2xR and
R^3 (5 of the remaining 7 geometries identified by
Thurstons geometrization programme must be the ou
tlying planets: all virtually solvable and very mu
ch full of life. We might think of these solvable
geometries as in some way the trivial cases. But t
hey have also been an inspiration both in algebra
and in geometry.
In this talk I will
take a survey that leads in a meandering way thro
ugh solvable infinite groups and culminates in a s
tudy of random walks on Cayley graphs including re
cent work joint with Lorensen as well as independe
nt results of Jacoboni.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
END:VEVENT
END:VCALENDAR