Differential Geometry and Topology

course: Constant scalar curvature Kähler metrics and stability of algebraic varieties

speaker: Richard Thomas (Imperial College)

abstract: In this first of two talks, I'll review the correspondence between stable holomorphic bundles and Hermitian-Yang-Mills connections, and explain the related conjectures of Yau, Tian, Fujiki & Donaldson on stable algebraic varieties and constant scalar curvature Kähler metrics. I will discuss Mumford's Geometric Invariant Theory notion of stability for algebraic varieties, and a modification - Tian's K-stability.

Good references for this material are Donaldson's papers Scalar curvature and projective embeddings, I (http:/projecteuclid.orgDienstUI1.0Summarizeeuclid.jdg1090349449) and Planck's constant in complex and almost-complex geometry, as well as Tian's book Canonical metrics in Kähler geometry.

In the second talk I will describe joint work with Julius Ross attempting to give an intrinsic geometric criterion for K- and Mumford-Chow- stability reminiscent of the slope criterion for stable bundles.

timetable:
Mon 13 Sep, 17:00 - 18:00, Sala Conferenze Centro De Giorgi
Tue 14 Sep, 15:30 - 17:00, Sala Conferenze Centro De Giorgi
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