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Title:
Topology of quadrature domains: 2D Coulomb gas with algebraic potential
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Abstract:
A large number of particles on the plane interacting by 2 dimensional Coulomb repulsion tend to condense over the region that we call droplet. Such droplets appear in random normal matrix theory and Hele-Shaw flows, and is closely related to quadrature domains. We study the topology of such droplets when the external potential is algebraic. The results have several applications, e.g. in the 2 dimensional inverse moment problem and in gravitational lensing. A joint work with Nikolai Makarov.
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