Quadrature Domains and Laplacian Growth in Modern Physics (07w5008)
Darren Crowdy (Imperial College London)
Bjorn Gustafsson (Royal Institute of Technology, Stockholm)
Mark Mineev-Weinstein (Federal University of Rio Grande do Norte, Brazil)
Mihai Putinar (University of California at Santa Barbara)
The following list summarizes some of the many topics, linked in various ways described above, that are to be discussed at the workshop. Particular emphasis will be given to the links between the traditional mathematical school of quadrature domains and Laplacian growth (1)-(5) and areas of modern physics (6)-(10) where new applications have recently been noticed.
(1) classical quadrature domains (algebraic domains) and the Schwarz function;
(2) geometric function theory, Riemann surfaces and algebraic curves;
(3) Laplacian growth, deformation of quadrature domains, Hele Shaw flow, Loewner theory;
(4) questions of balayage and gravi-equivalence in potential theory;
(5) operator theory, sums of squares and the exponential transform;
(6) integrable systems theory: the dispersionless Toda hierarchy, the universal Whitham hierarchy and the Benney hierarchy;
(7) random matrix theory;
(8) diffusion-limited aggregation (DLA);
(9) 2D quantum gravity;
(10) string theory.