1er juillet 2020

Louis Ioos (Tel Aviv)
Applications of Berezin-Toeplitz quantization to Donaldson’s program in Kähler geometry

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Lieu : Demander le lien Zoom à jean-michel.bismut@u-psud.fr

Résumé : I will show how Berezin-Toeplitz quantization can be used to simplify and extend Donaldson’s proof
of existence and smooth convergence of balanced metrics to the Kähler metric of constant scalar curvature on a polarized manifold. This is of specific interest in the case of canonically balanced metrics converging to the polarized Kähler-Einstein metric, where only weak convergence results were known. I will then show how this allows to compute the rate of convergence of Donaldson’s iterations to the balanced product in various settings.
This approach is based in particular on the asymptotics of the spectral gap of the Berezin transform, which were computed in a joint work with V. Kaminker, L. Polterovich and D. Shmoish.

Applications of Berezin-Toeplitz quantization to Donaldson’s program in Kähler geometry  Version PDF