Victor Buchstaber (Steklov Mathematical Institute and University of Manchester)
Theory of Abelian functions was a central topic of the 19th century mathematics. In mid-seventies of the last century a new wave of investigation in this field arose in response to the discovery that Abelian functions provide solutions of a number of challenging problems of modern Theoretical and Mathematical Physics.
In a cycle of our joint papers with V. Enolskii and D. Leykin we have developed a theory of multivariate sigma-function, an analogue of the classic Weierstrass sigma-function.
In the talk I will describe solutions of some important differential equations in terms of two-dimensional sigma-functions.