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The spherical model with two external charges.

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CATW01 - The complex analysis toolbox: new techniques and perspectives

I will discuss a model from electrostatics where N charged
particles with charge 1/N distribute themselves over the unit sphere
in the presence of a finite number of fixed charges. In the
large N limit the particles concentrate on a part of the sphere
with uniform density. This is the droplet.

After stereographic projection, this model is analyzed
in the complex plane with tools from logarithmic potential theory.
For the case of two equal charges we compute a mother body, which
is then used to determine the droplet explicitly.

This is joint work Juan Criado del Rey.

This talk is part of the Isaac Newton Institute Seminar Series series.

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