Recent breakthrough in the theory of 2D growth, due to application of analytic theory of stochastic conformal mappings, opened new prospectives for solution of fundamental long-standing problems in the studies of interface dynamics and pattern formation. The research field has been enriched by new effective approaches, emerged from theory of integrable systems and analytic function theory, to deal with dynamics of a moving front between two distinct phases driven by a harmonic scalar field as well as for description of static cluster patterns in models of statistical mechanics and random matrices. The aim of the present project is to address the basic questions of theory of unstable and stochastic interfaces, integrating recent achievements in stochastic conformal mappings and complex dynamics into the field of research. Connecting three subjects: Laplacian growth, stochastic Loewner chains and theory of integrable systems, we expect to advance interface dynamics and account for its basic physical features.
Call for proposal
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