The conference will present the new developments in the study of
canonical/special metrics that can be considered as uniformisers of
complex geometry (like constant scalar curvature Kahler metrics,
extremal Kahler metrics, Kahler-Einstein metrics, Kahler-Ricci
solitons, Sasaki-Einstein metrics, Bergman metrics, balanced metrics
...). It will also reflect the diversity of analytic methods
to construct such metrics (flows, continuity methods, gluing
techniques, ...)
and the diversity of varieties where they live (compact and non compact Kahler
manifolds, Sasaki manifods, toric manifolds, spherical manifolds, orbifolds,...).
Finally, a part of the conference will be concerned with the relationship
between the existence of canonical metrics and algebraic conditions coming from
Geometric Invariant Theory.