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SUMMARY:Ricci flow and the determinant of the Laplacian on non-compact sur
 faces - Pierre Albin (Paris VI Jussieu\, Urbana-Champaign)
DTSTART:20101122T170000Z
DTEND:20101122T180000Z
UID:TALK28026@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:The determinant of the Laplacian is an important invariant of 
 closed\nsurfaces and has connections to the dynamics of geodesics\, Ricci 
 flow\, and physics. Its definition is somewhat intricate as the Laplacian 
 has infinitely many eigenvalues. I'll explain how to extend the determinan
 t of the Laplacian to non-compact surfaces where one has to deal with addi
 tional difficulties like continuous spectrum and divergence of the trace o
 f the heat kernel. On surfaces (even non-compact) this determinant has a s
 imple variation when the metric varies conformally. I'll explain how to us
 e Ricci flow to see that the largest value of the determinant occurs at co
 nstant curvature metrics. This is joint work with Clara Aldana and Frederi
 c Rochon.
LOCATION:CMS\, MR5
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