Quantum Geometry, Stochastic Geometry, Random Geometry, you name it: June 15 – 19, 2015

Organized by Robert Berman, Semyon Klevtsov, Paul Wiegmann, and Steve Zelditch

Dates: June 15 – 19, 2015

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This workshop is devoted to random surfaces, shapes and fields, in both physics and geometry. In statistical mechanics in two spatial dimensions random fields are associated with critical fluctuations of random geometric objects such as curves and surfaces. Recently similar mathematical structures have been observed in the theory of quantum Hall effect. These problems call for a quest of further and deeper understanding of measures of random geometrical objects. In higher dimensions, the natural generalization of stochastic conformal geometry is to Kahler manifolds. Correlation functions of random fields on general Kahler manifolds are related to Bergman kernels. In general dimensions, Bergman kernels arise as covariance kernels of Gaussian holomorphic random fields, whose zeros and critical points are of interest both in mathematics and physics. Bergman kernels give an alternative approach to random surfaces by way of random Bergman metrics, defined by random holomorphic embeddings into projective space. The workshop will include talks by physicists and mathematicians on each topic.

This workshop is a part of the Spring 2015 program, Large N limit problems in Kahler Geometry, which is organized by Robert Berman, Semyon Klevtsov, Paul Wiegmann, and Steve Zelditch. This program takes place from April 20 – June 19, 2015.