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SUMMARY:Eric Samperson (UIUC)
DTSTART:20200609T153000Z
DTEND:20200609T160000Z
DTSTAMP:20260423T003233Z
UID:GaTO/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/14/">Ho
 w helpful is hyperbolic geometry?</a>\nby Eric Samperson (UIUC) as part of
  Geometry and topology online\n\n\nAbstract\nHyperbolic geometry serves du
 al roles at the intersection of group theory and three-manifold topology. 
 It plays the hero of group theory — rescuing the field from a morass of 
 uncomputability — but the anti-hero of low-dimensional topology—seemin
 gly responsible for much of the complexity of three-manifolds. Where do th
 ese roles overlap?\n\nI’ll give examples of group-theoretic invariants o
 f three-manifolds (or knots) that are NP-hard to compute\, even for three-
 manifolds (or knots) that are promised to be hyperbolic. The basic idea is
  to show that the right-angled Artin semigroups of reversible circuits (a 
 kind of combinatorial abstraction of particularly simple computer programs
 ) can be quasi-isometrically embedded inside mapping class groups. Recent 
 uniformity results concerning the coarse geometry of curve complexes play 
 a key role.\n\nThis is joint work with Chris Leininger that builds on prev
 ious work with Greg Kuperberg.\n
LOCATION:https://researchseminars.org/talk/GaTO/14/
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