Geometric quantisation and extremal Kähler metrics

Yoshinori Hashimoto
I2M, Aix-Marseille Université

Date(s) : 09/10/2017   iCal
14 h 00 min - 15 h 00 min

Existence of canonical Kähler metrics, such as Kähler-Einstein metrics or more generally extremal Kähler metrics, has been studied intensively in recent years. Although this amounts to solving a nonlinear PDE, it is known to have a deep connection to a purely algebro-geometric notion called K-stability, defined in terms of Geometric Invariant Theory. In the first part of this talk, we shall review the background and introduce Donaldson’s approach to this problem with ideas from geometric quantisation. In presence of symmetries this approach does not naively work, and in the second part of the talk we shall introduce a new “quantising” equation to extend Donaldson’s result in presence of symmetries, and discuss its implications to relative K-stability.


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