Date: Friday, January 24, 2014
Location: 3866 East Hall (3:00 PM to 4:00 PM)
Title: Imaginary time flow in geometric quantization and in Kahler geometry, degeneration to real polarizations and tropicalization
Abstract: We will recall the problem of dependence of quantization of a symplectic manifold on the choice of polarization and study its relation with geodesics in the space Kahler metrics. Complex one parameter subgroups of the "group" of complexified hamiltonian symplectmorphisms appear naturally in this context.
For some classes of symplectic manifolds we will describe geodesic rays of Kahler structures degenerating to real polarizations and study the associated metric collapse. Each such ray selects a basis of holomorphic sections which converge to distributional sections supported on BohrSommerfeld fibers as the geodesic time goes to infinity.
We will review the tropicalization of amoebae of hypersurfaces on (C^*)^n and will show that the analogous geodesic rays give a natural extension of tropicalization to toric varieties and hypersurfaces on toric varieties.
Files:
Speaker: Jose Cidade Mourao
Institution: Tecnico Lisboa, University of Lisbon
Event Organizer: Dan Burns geometryseminar@umich.edu
