Manchester Geometry Seminar 2001/2002

Uniformization of elliptic curves by Weierstrass functions has important applications in the modern problems of soliton theory. In the recent papers by the speaker, V. Z. Enol'skii and D. V. Leikin the classical Weierstrass uniformization was extended to a wide class of algebraic curves. In the talk we discuss the geometric aspects of this result and its application. The plan of the talk is as follows:

1. Main definitions and constructions
2. Matrix realizations of universal fibrations: the case of hyperelliptic curves and the case of trigonal curves
3. Kleinian sigma functions
4. Uniformizations of universal spases of Jacobians
5. Applications