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International conference "Geometrical Methods in Mathematical Physics"
December 15, 2011 14:45–15:30, Moscow, Lomonosov Moscow State University
 


An infinite-dimensional Frobenius manifold and the extended 2D Toda hierarchy

G. Carlet

International School for Advanced Studies (SISSA)
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Flash Video 292.5 Mb
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Adobe PDF 252.5 Kb

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G. Carlet


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Abstract: We consider the recent advances in the programme of extending the Frobenius manifolds techniques to integrable PDE's with two spatial variables. First, we review the construction of an infinite-dimensional Frobenius manifold structure $M$ on a 2-vector bundle on the space of simple analytic curves in the complex plane. Second, we show that it is possible to explicitly solve the operator-valued singular linear system on the complex plane associated with the deformed flat connection of the Frobenius manifold. This solution defines a principal hierarchy which extends the dispersionless 2D Toda hierarchy.

Materials: gmmp2011_gcarlet.pdf (252.5 Kb)

Language: English

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