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Dienstag, 10.04.2018 | 16.00 - 18.00 Uhr | D2

Oberseminar: Prof. Dr. J. Mourao (IST Lissabon)

Titel: Complex symplectomorphisms, Kähler geodesics and representation theory

Dieser Vortrag findet statt im Rahmen des Oberseminars "Algebraische Methoden der harmonischen Analysis"

Abstract: The geodesics for the Mabuchi metric on the space H of Kähler metrics on a compact symplectic manifold M correspond to solutions of a homogeneous complex Monge-Ampere (HCMA) equation. The space H is an infinite dimensional analogue of the symmetric spaces of noncompact type G_C/G for compact Lie groups G. In H the role of G is being played by the group of Hamiltonian symplectomorphisms.

We will describe a method for reducing the relevant Cauchy problem for the HCMA equation with analytic initial data to finding a related Hamiltonian flow followed by a "complexification".

For Hamiltonian G-spaces, with G-invariant Kähler structure, the geodesic corresponding to the norm square of the moment map or its Hamiltonian flow in imaginary time (= gradient flow for the changing metric following the geodesic) leads to the convergence of the holomorphic sections to sections supported on Bohr-Sommerfeld leaves.

For M=T*G, starting from the vertical or Schrödinger polarization, one obtains the Segal-Bargmann-Hall coherent state transform.

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