Extremal Metrics and Relative K-Stability

Gluing technics in Complex Geometry, University of Bath (UK)

Gluing is one of very few general methods to construct special Riemannian metrics (Einstein, constant scalar curvature, ...)
on compact manifolds, by combining geometric intuition and explicit local solutions with analytic singular perturbation techniques.
This method is particularly effective in the setting of complex geometry: it can be used to test the Yau-Tian-Donaldson conjecture.
In fact, explicit solutions and gluing provide the only known tools to say anything at all beyond the recently resolved Kähler-Einstein case of this conjecture.
There has been a steady stream of interesting new results in this direction in recent years and the area seems poised for further development.

July 13th to July 17th 2015

D.M.J. Calderbank, University of Bath,

H-J. Hein, University of Maryland,

E. Legendre, Université Fédérale Toulouse Midi-Pyrénées,

Lectures given by:
Claudio Arezzo (ICTP, Trieste, Italy)
Lorenzo Foscolo (Stony Brook, US)
Paul Gauduchon (École Polytechnique, France)
Christiano Spotti (Cambridge, UK)
Hans-Joaquim Hein (University of Mayland, US)
Carl Tipler (Université de Bretagne orientale, France)