University of Birmingham > Talks@bham > Algebra Seminar > Finite Group Actions on Compact Riemann Surfaces

Finite Group Actions on Compact Riemann Surfaces

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If you have a question about this talk, please contact David Craven.

The problem of determining the distinct finite group actions on a compact Riemann surface of a fixed genus is a classical problem in complex analysis. Though there has been tremendous progress in the last few years toward solving this problem, it is widely accepted that a complete answer is intractable due to its computational complexity. Therefore, much current research in this area focuses on easier but more amenable problems which provide insight into the more general problem.

In this talk, we introduce a new and simpler way to consider this problem. Though this new approach ignores much of the geometric structure of an automorphism group, it does provide a new and elegant way to represent group actions which we shall illustrate through a number of classical examples. We shall finish by showing that this very elementary way of describing group actions is in fact sufficient to prove that for a fixed genus σ ≥ 6, there is minimally a quadratic lower bound in the genus σ for the number of distinct group actions on a surface of genus σ.

This talk is part of the Algebra Seminar series.

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