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Title:
Integrability of Laplacian growth in a channel and Hurwitz numbers
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Abstract:
"The idea of ""convolution symmetries"" and ""convolution flows"" in the context of integrable hierarchies is very natural when the dynamics are viewed, as in the Sato-Segal-Wilson approach to the KP hierarchy, as commuting flows on an infinite Hilbert spaceGrassmannian. Since convolution products on the Hilbert space of square integrable functions, say, on the unit circle are represented within the natural orthonormal basis by a diagonal operator, such flows are, in some sense, more natural than the ""shift"" flows generating
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