Sorbonne Université CNRS Paris Diderot

Séminaire d’Analyse et Géométrie

Interface behavior of Partial Bergman Kernel

Peng Zhou - IHES

mardi 20 février 2018 à 14:00
Barre 15-25, 5ème étage, salle 02

Partial Bergman kernels are kernels of orthogonal projections onto subspaces of holomorphic sections of the 𝑘-th power of an ample line bundle L over a Kahler manifold M. The subspaces of this talk are spectral subspaces {H𝑘 < E} of the Toeplitz quantization H𝑘 of a smooth Hamiltonian H ∶ M → R. It is shown that the relative partial density of states converges to the characteristic function of the domain A, where A={H < E}. Moreover it is shown that this partial density of states exhibits ‘Erf’-asymptotics along the boundary of A, that is, the density profile asymptotically has a Gaussian error function shape interpolating between one and zero. Such ‘erf’-asymptotics are a universal edge effect. This is based on joint work with Steve Zelditch

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