XXIX Workshop on Geometric Methods in Physics | 27.06-03.07.2010 |

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## Emma Previato## Sigma function and dispersionless hierarchiesRiemann surfaces (smooth compact curves) traditionally provide explicit solutions to equations of mathematical physics via the Riemann theta function. Klein and H.F. Baker in the 19th century introduced a version of it, the sigma function, which is more directly related to algebraic data of the curve. The sigma function, its order of vanishing on the Wirtinger stratification of the Jacobian, and its (characteristic) differential equations have been the focus of much recent work. In this talk we illustrate the current knowledge of the sigma function and present an untraditional way of giving explicit solutions to dispersionless hierarchies (e.g., dKP, Burgers-Hopf). |

University of Bialystok |

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