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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Ricci flow and the determinant of the Laplacian on
non-compact surfaces - Pierre Albin (Paris VI Jus
sieu\, Urbana-Champaign)
DTSTART;TZID=Europe/London:20101122T170000
DTEND;TZID=Europe/London:20101122T180000
UID:TALK28026AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28026
DESCRIPTION:The determinant of the Laplacian is an important i
nvariant of closed\nsurfaces and has connections t
o the dynamics of geodesics\, Ricci flow\, and phy
sics. Its definition is somewhat intricate as the
Laplacian has infinitely many eigenvalues. I'll ex
plain how to extend the determinant of the Laplaci
an to non-compact surfaces where one has to deal w
ith additional difficulties like continuous spectr
um and divergence of the trace of the heat kernel.
On surfaces (even non-compact) this determinant h
as a simple variation when the metric varies confo
rmally. I'll explain how to use Ricci flow to see
that the largest value of the determinant occurs a
t constant curvature metrics. This is joint work w
ith Clara Aldana and Frederic Rochon.
LOCATION:CMS\, MR5
CONTACT:Prof. Mihalis Dafermos
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