XXVIII Workshop on Geometric Methods in Physics 28.06-04.07.2009

Victor Buchstaber

Heat equations and sigma functions

The 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 to a number of challenging problems of modern Theoretical and Mathematical Physics.

In the cycle of our joint papers with V.Enolski and D.Leykin we have developed a theory of multivariate sigma-function, an analogue of the classic Weierstrass sigma-function.

The talk is based on the joint papers with D.Leykin and E. Bunkova.

We will describe the solutions of some important differential equations in terms of sigma-functions.