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SUMMARY:A tale of two norms. - Nathan Dunfield\, UIUC
DTSTART:20170208T160000Z
DTEND:20170208T170000Z
UID:TALK69186@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:The first cohomology of a hyperbolic 3-manifold has two natura
 l norms: the Thurston norm\, which measure topological complexity of surfa
 ces representing the dual homology class\, and the harmonic norm\, which i
 s just the L^2 norm on the corresponding space of harmonic 1-forms.  Berge
 ron-Sengun-Venkatesh recently showed that these two norms are closely rela
 ted\, at least when the injectivity radius is bounded below.\n\nTheir work
  was motivated by the connection of the harmonic norm to the Ray-Singer an
 alytic torsion and issues of torsion growth.  After carefully introducing 
 both norms and the connection to torsion growth\, I will discuss new resul
 ts that refine and clarify the precise relationship between them\; one too
 l here will be a third norm based on least-area surfaces.  This is joint w
 ork with Jeff Brock.
LOCATION:MR13
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