BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Symmetries of the free-factor complex and commensurator rigidity 
   - Martin Bridson (University of Oxford)
DTSTART:20230519T124500Z
DTEND:20230519T134500Z
UID:TALK199153@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:A commensuration of a group G is an isomorphism between finite
 -index subgroups of G. Equivalence classes of such maps form a group\, who
 se importance first emerged in the\nwork of Margulis on arithmetic lattice
 s in semisimple Lie groups. Drawing motivation from this classical setting
  and from the study of mapping class groups of surfaces\, I shall\nexplain
  why\, when N is at least 3\, the group of automorphisms of the free group
  of rank N is its own abstract commensurator. Similar results hold for cer
 tain\nsubgroups of Aut(F_N). A key element in the proofs is a non-abelian 
 analogue of the Fundamental Theorem of Projective Geometry\, in which proj
 ective subspaces are replaced by the \nfree factors of a free group. This 
 last result is the content of a long-running project with Mladen Bestvina\
 , while the results on commensurators are the content of a similarly\nexte
 nded project with Ric Wade. If time allows\, I shall discuss related open 
 questions
LOCATION:MR13
END:VEVENT
END:VCALENDAR