Canonical metrics on Kähler manifolds and holomorphic vector bundles

This is the course webpage for the graduate course NFMV025: Canonical metrics on Kähler manifolds and holomorphic vector bundles given at Chalmers/University of Gothenburg in the 2022-23 academic year. Registration can be done here.

There will be an introductory lecture on Thursday the 15th of September, 09:00-11:00 in MVL15. The course start is then in the week beginning Monday the 26th of September. We will decide the time for the lectures during the introductory lecture.

Notes are available here. They will be updated as the course goes on.

Learning goals:

• Hodge theory on Kähler manifolds

• Uniformisation theorem

• Existence of Kähler-Einstein metrics on canonically polarised/Calabi-Yau manifolds

• The classical Futaki invariant

• The LeBrun-Simanca openness theorem for cscK/extremal metrics

• The infinite dimensional moment map picture for the scalar curvature and K-stability as an obstruction to the existence of cscK metrics

• The Hitchin-Kobayashi correspondence for holomorphic vector bundles