Quantization in stages and canonical metrics

Abstract: In this talk, I will introduce the notion of quantization in stages, which lies at the basis of fundamental physical set-ups such as the Stern-Gerlach experiment, and explain how it can be realized over compact symplectic phase spaces via the use of Berezin-Toeplitz quantization of vector bundles. In particular, I will introduce and show how to compute the associated quantum noise. I will then describe an application to Hermite-Einstein metrics on stable vector bundles over a projective manifold, and if time permits, I will show how a refinement of these results in the case of the trivial line bundle can be applied to Kähler metrics of constant scalar curvature.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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