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SUMMARY:Simplicial complexity - Shmuel Weinberger (University of Chicago)
DTSTART:20250711T104500Z
DTEND:20250711T114500Z
UID:TALK232876@talks.cam.ac.uk
DESCRIPTION:A basic measure of the complexity of a manifold is the minimum
  number of simplices in a triangulation.&nbsp\; I will explain how using L
 ^2 cohomology\, hyperbolization and related ideas\, one can get bounds on 
 this for certain lens spaces (and homotopy lens spaces) - joint work with 
 G. Lim.&nbsp\; Assuming a bound on local geometry this&nbsp\;result could 
 be deduced analytically from work of Calabi and Cheeger-Gromov\, but the g
 eneral case seems to require (for me) additional geometric input\,&nbsp\;e
 ssentially&nbsp\;proving a result about positively curved manifolds by non
 positively curved geometry!&nbsp\; If there is time\, I will try to put th
 is into a conjectural perspective on how simplicial complexity interacts w
 ith surgery theory (and why the standard einsatz of simplicial complexity 
 being a proxy for volume is wrong) and explain some obstacles (arising in 
 work with F. Manin) to realizing such a vision.
LOCATION:Seminar Room 1\, Newton Institute
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