# Manchester Geometry Seminar 2008/2009

**Thursday 4 December 2008. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm*
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The Heat Equations and the Sigma-Function of the Universal Genus Two Curve

Victor Buchstaber (Steklov Mathematical Institute and University of Manchester)

`Victor.Buchstaber@manchester.ac.uk`

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.