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In broad terms the aim of this proposal is to introduce a new probabilistic approach to the study of Kähler-Einstein (K-E) metrics on complex manifolds. A precise procedure, based on a blend of Statistical Mechanics, Pluripotential theory and Kähler Geometry. will be used to show that• when a K-E metric exists on a complex manifold X it can be obtained from the “largeN limit” of certain canonical ...

There exist more than 7000 rare diseases worldwide and the European Society of Paediatric Oncology stated that 75% of rare diseases affect children and 30% of rare disease patients die before the age of five. Usual statistical methods for proving efficacy and safety of therapies fail to provide cost-efficient and reliable results in small populations. There is a pressing need to integrate a broad ...