A transcendental view of the space of algebraic Riemann surfaces

Abstract

The subject of my lecture is not a large-scale and general theory but rather a special problem in conformai mapping. By way of justification for bringing it to the attention of a broader audience I may cite, first of all, its deep nature and honorable origin-the problem originated in Riemann's memoir Secondly, it is intimately bound up with a variety of topics of more general interest: conformai mapping with particular reference to extremal problems, several complex variables, and partial differential equations, on the one hand; topology and algebraic geometry, on the other and, in particular aspects, even group representations and arithmetic.