Australian Geometric Topology Webinar: Lanier -- Mapping class groups and dense conjugacy classes

Australian Geometric Topology Webinar: 
’Mapping class groups and dense conjugacy classes’ 

Date and time: Wednesday 15 May May, 13:00-14:00 AEST 
Location: Online via Zoom, email [email protected] 

Speaker: Justin Lanier (University of Sydney)
Abstract: I’ll start by discussing some examples of topological groups that have dense
conjugacy classes, so that there exists an element that well approximates every element
in the group, up to conjugacy.  I’ll also give an overview of infinite-type surfaces
(those with infinite genus or infinitely many punctures) and the emerging study of their
mapping class groups.  One difference from the finite-type setting is that these mapping
class groups come with natural non-discrete topologies.  I’ll discuss joint work with
Nick Vlamis where we characterize which surfaces have mapping class groups with dense
conjugacy classes.  I’ll also discuss our follow-up work where we do the same for
finite index subgroups of these mapping class groups, as well as for homeomorphism
groups of surfaces.