Riemann surfaces are fascinating topological objects with extra structure which allows us to translate ideas from analysis onto them. Additionally, groups can describe ways to permute the elements of a Riemann surface through a process called a group action. To give you a sense of what my field of research entails, we first need to understand group actions and Riemann surfaces. While this may seem like a tall order, you can grasp the ideas of these topics with just a first semester undergraduate course in both algebra and analysis, along with a basic knowledge of the complex numbers (such as roots of unity). An undergraduate course in topology may aid your understanding, but I define key ideas along the way.

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Group Actions and Riemann Surfaces

  • Jennifer Paulhus

摘要

Riemann surfaces are fascinating topological objects with extra structure which allows us to translate ideas from analysis onto them. Additionally, groups can describe ways to permute the elements of a Riemann surface through a process called a group action. To give you a sense of what my field of research entails, we first need to understand group actions and Riemann surfaces. While this may seem like a tall order, you can grasp the ideas of these topics with just a first semester undergraduate course in both algebra and analysis, along with a basic knowledge of the complex numbers (such as roots of unity). An undergraduate course in topology may aid your understanding, but I define key ideas along the way.