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SUMMARY:Edgar Bering (San Jose State University)
DTSTART:20260507T123000Z
DTEND:20260507T133000Z
DTSTAMP:20260623T074559Z
UID:GaTO/145
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/145/">M
 odulii of solenoids and commensurations of the free group</a>\nby Edgar Be
 ring (San Jose State University) as part of Geometry and topology online\n
 \nLecture held in Room B3.02 in the Zeeman Building\, University of Warwic
 k.\n\nAbstract\nThe abstract commensurator of a group Comm(G) is the group
  of isomorphisms between finite-index subgroups\, up to the equivalence of
  agreement on a common finite-index domain. Commensurators famously appear
  in Margulis' arithmeticity theorem\, and for a suitable Lie group the abs
 tract commensurator detects the arithmeticity of lattices. Notably\, PSL_2
 (R) is not suitable: every lattice is virtually a free or closed surface g
 roup\, and the abstract commensurator fails to detect arithmeticity in thi
 s setting. Other methods are required to study the abstract commensurator 
 of finitely generated free or surface groups. Biswas\, Nag\, and Sullivan 
 developed a universal Teichmuller theory" and approached the abstract comm
 ensurator of a surface group with ideas from mapping class group theory. I
  will introduce\, following Culler and Vogtmann's outer space\, the moduli
 i space of metric graph solenoids. This space is equivalent to an appropri
 ate direct limit of auter spaces (base points turn out important)\, and ha
 s a global structure coming from Leighton's theorem on graph covers. Once 
 the audience is situated in this space I will use the natural action of th
 e abstract commensurator Comm(F) on this space to reveal exciting features
  of Comm(F). This is joint work with Daniel Studenmund.\n
LOCATION:https://researchseminars.org/talk/GaTO/145/
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