BEGIN:VCALENDAR
PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
 M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20261104T233243Z
DTSTART:20261111T133000Z
DTEND:20261111T143000Z
SUMMARY:Pure maths colloquium - Richard Webb
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}chp-mw2ly5h
 i-46fc2l
DESCRIPTION:Speaker: Richard Webb (University of Manchester)\n\nTitle: Fi
 nding surface subgroups in mapping class groups\n\nAbstract: Many infini
 te groups can be studied by associating geometric spaces to them. Free g
 roups\, for example\, act naturally on trees. The class of hyperbolic gr
 oups generalises this picture\, in that they are modelled on spaces wher
 e geodesic triangles are uniformly slim\, a fact that is true for trees.
  I will explain a few ways in which their geometry helps us understand t
 heir algebra. These groups play a central role in low-dimensional topolo
 gy and geometric group theory. Beyond free groups\, basic examples are t
 he surface groups: the fundamental groups of closed orientable surfaces 
 of genus at least two. These groups act on the hyperbolic plane.\n\nWhil
 e many infinite groups contain an abundance of free subgroups\, finding 
 surface subgroups in general is notoriously difficult. In this talk\, I 
 will focus on mapping class groups\, whose elements are homeomorphisms o
 f a surface to itself up to continuous deformation. Although mapping cla
 ss groups are generally not hyperbolic\, they exhibit many features in c
 ommon with hyperbolic groups. I will explain how to find surface subgrou
 ps of mapping class groups with desirable geometric properties. Our cons
 truction also produces surface bundles over surfaces whose total spaces 
 have hyperbolic fundamental groups. Joint work with Alex Wright.\n\nRoom
 : Alan Turing Building G.205\n\nThe talk will be followed by a reception
  outside of FA1.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
END:VEVENT
END:VCALENDAR