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UID:20251121T093946EST-7363HxMMJm@132.216.98.100
DTSTAMP:20251121T143946Z
DESCRIPTION:Spectral geometry of manifolds with conic singularities.\n\nIn 
 1966 Mark Kac asked his famous question “Can one hear the shape of a drum?
 ” that corresponds to the following mathematical problem. Suppose we are g
 iven a sequence of eigenvalues of some geometrical operator on a manifold.
  What information about geometry of the manifold can be derived from the s
 equence of eigenvalues? If a manifold is allowed to have singularities\, t
 hen one can ask a similar question “Can one hear the presence of a singula
 rity?”. In the talk we investigate this problem for manifolds with conic s
 ingularities. Our main tool is small-time asymptotic expansion of the heat
  trace. We begin the talk with an overview of the heat kernel of Laplace o
 perator on a manifold. In case of a compact smooth manifold the heat trace
  expansion gives some geometrical information such as dimension\, volume a
 nd total scalar curvature of the manifold. In case of a manifold with coni
 c singularities the heat trace expansion is more difficult than in the smo
 oth case. Using Singular Asymptotics Lemma of Bruening and Seeley we obtai
 n information about a singularity from the heat trace expansion.\n
DTSTART:20170317T173000Z
DTEND:20170317T183000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Asilya Suleymanova\, Humbolt
URL:/mathstat/channels/event/asilya-suleymanova-humbol
 t-266914
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