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SUMMARY:Quantisation and the Hessian of Mabuchi energy - Joel Fine (Univer
 sité Libre de Bruxelles)
DTSTART:20120412T133000Z
DTEND:20120412T143000Z
UID:TALK36842@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:Let L be an ample line bundle over a compact complex manifold.
  In Kähler quantisation one approximates the space H of Kähler metrics i
 n c_1(L) by the spaces B_k of Hermitian innerproducts on H<sup>0</sup>(X\,
 L<sup>k</sup>).   Following Donaldson\, we know that Mabuchi energy E on H
  is "quantised" by balancing energy F_k\, a function on B_k. \n\nI will ex
 plain a result in this vein\, namely that the\nHessian D of E\, a 4th orde
 r self-adjoint elliptic operator on functions\, is quantised by the Hessia
 ns P_k of the F_k\, operators on the space of Hermitian endomorphisms of H
 ^0 (X\,L<sup>k</sup>) defined purely in terms of projective embeddings. In
  particular\, the eigenvalues and eigenspaces of P_k converge to those of 
 D.  I will explain applications of this result as well as\naspects of its 
 proof. 
LOCATION:MR2
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