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UID:7a6cfd3164658904c85571077cfe2fbf
CATEGORIES:Geometric Analysis Seminar
CREATED:20240329T153243
SUMMARY:On a generalization of Geroch's conjecture
LOCATION:Hill-705
DESCRIPTION:Abstract: The theorem of Bonnet-Myers implies that manifolds with topology 
 $M^{n-1}times S^1$ do not admit a metric of positive Ricci curvature, while
  the resolution of Geroch's conjecture shows that the torus $T^n$ does not 
 admit a metric of positive scalar curvature. In this talk I will introduce 
 a new notion of curvature which interpolates between Ricci and scalar curva
 ture (so-called $m$-intermediate curvature) and use stable weighted slicing
 s to show that for $nle7$ the manifolds $M^{n-m}times T^m$ do not admit a m
 etric of positive $m$-intermediate curvature. This is joint work with Simon
  Brendle and Florian Johne.\n
X-ALT-DESC;FMTTYPE=text/html:<p><span style="color: #000000; font-family: arial, helvetica, sans-serif; 
 font-size: 16px; font-style: normal; font-weight: 400; letter-spacing: norm
 al; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; 
 widows: 2; word-spacing: 0px; white-space: normal; background-color: #fffff
 f; float: none;">Abstract: The theorem of Bonnet-Myers implies that manifol
 ds with topology $M^{n-1}times S^1$ do not admit a metric of positive Ricci
  curvature, while the resolution of Geroch's conjecture shows that the toru
 s $T^n$ does not admit a metric of positive scalar curvature. In this talk 
 I will introduce a new notion of curvature which interpolates between Ricci
  and scalar curvature (so-called $m$-intermediate curvature) and use stable
  weighted slicings to show that for $nle7$ the manifolds $M^{n-m}times T^m$
  do not admit a metric of positive $m$-intermediate curvature. This is join
 t work with Simon Brendle and Florian Johne.</span></p>
CONTACT:Sven Hirsch
DTSTAMP:20260828T110908
DTSTART;TZID=America/New_York:20240402T145000
DTEND;TZID=America/New_York:20240402T155000
SEQUENCE:0
TRANSP:OPAQUE
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