SYLLABUS MATH 519: Riemann surfaces: analysis, geometry, and arithmetic

  • Riemann surfaces are a meeting ground for a variety of areas of pure mathematics such as complex analysis, non-Euclidean geometry, and number theory. This course has as its only prerequisites a (graduate or even undergraduate) complex analysis course and a (graduate or even undergraduate) Abstract Algebra course. I will cover analytic aspects of Riemann surfaces (Abelian integrals, de Rham cohomology), geometric aspects (ramification, uniformization via Fuchsian groups), and arithmetic aspects (counting points of polynomial congruences). The necessary tools will be introduced as we go. There is no textbook.
  • Grading will be based upon attendance.
  • Note. Qualified students with disabilities needing appropriate academic adjustments should contact me as soon as possible to ensure your needs are met in a timely manner. Handouts are available in alternative accessible formats upon request.
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