Extremal Kaehler metrics (09w5027)


Vestislav Apostolov (UQAM)

Claudio Arezzo (ICTP)

Xiuxiong Chen (University of Wisconsin)

(Imperial College)


The Banff International Research Station will host the "Extremal Kaehler metrics" workshop next week, June 28 - July 3, 2009.

In mathematics, many striking problems and their solutions lie at the interface of seemingly separate disciplines. This phenomenon is well exemplified by the problem, first proposed by Calabi, of finding a canonical Kaehler metric, called extremal Kaehler metrics, in a given cohomology class. The techniques relevant to this problem come from Geometric Analysis, Differential Geometry and Algebraic Geometry.

In rough terms, the extremal Kaehler metrics are natural generalisations of metrics of constant Gauss curvature on 2-dimensional surfaces. From the point of view of global analysis, they are solutions to a fully non-linear 4th order PDE of Monge-Ampere type, for which no general methods are currently available. Particular cases include Kaehler metrics of constant scalar curvature (CSC) and Kaehler--Einstein metrics (KE), the study of which is in the forefront of Kaehler geometry over the last decades.

The main objective of the workshop is to brought together researchers in the separate but related fields of geometric analysists, differential geometry and algebraic geometry to focus on a specific, hard problem at the forefront of current research, and make a progress.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).