Rice University Department of Mathematics Colloquium

Geometry of Riemann surfaces and norms on pluri-canonical forms.

4:00 pm Thursday, November 5, 2015
Stergios Antonakoudis (Cambridge University)

Abstract: Every closed Riemann surface is equipped with a natural norm on the space of holomorphic quadratic differentials. In his pioneering 1971 paper, H. L. Royden proved the remarkable theorem that this norm uniquely determines the Riemann surface and initiated the study of these norms as natural invariants of Riemann surfaces. In this talk, we will study the geometry of these norms and their generarizations to pluri-canonical forms and discuss their applications to the geometry of Riemann surfaces and their moduli spaces. We will also discuss analogous norms for higher dimensional varieties and prove a conjecture of S.-T. Yau, generalising Royden's theorem for complex varieties of general type.

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