BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Shmuel Weinberger (University of Chicago)
DTSTART:20230503T111000Z
DTEND:20230503T123000Z
DTSTAMP:20260423T022711Z
UID:GDS/81
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDS/81/">Tor
 sion\, L^2 cohomology and complexity</a>\nby Shmuel Weinberger (University
  of Chicago) as part of Geometry and Dynamics seminar\n\n\nAbstract\nAtiya
 h introduced real valued L^2 betti numbers as a way of\nunderstanding the 
 (usually infinite dimensional) cohomology of\nuniversal covers of finite c
 omplexes.  As far as anyone knows these\nare always integers for torsion f
 ree fundamental group\, but for groups\nwith torsion very much more exotic
  possibilities arise.\n\nWe will use this and an invariant of Cheeger and 
 Gromov to see that\nwhenever an oriented smooth manifold of dimension 4k+3
  has torsion in\nits fundamental group\, there are many other manifolds ho
 motopy\nequivalent but not diffeomorphic to it and that in the known\nsitu
 ations where betti numbers can be irrational there is even an\ninfinitely 
 generated group of such!  And\, I will also use this\ninvariant to explain
  how many simplices (roughly) it takes to build a\nstandard Lens space.  T
 his is based on old work with Stanley Chang\,\nand recent work with Geunho
  Lim.\n
LOCATION:https://researchseminars.org/talk/GDS/81/
END:VEVENT
END:VCALENDAR