Math 234, Riemann Surfaces, Fall 2015

• Lectures: TTh 10:00-11:45pm, McHenry 1279

• Text: Riemann Surfaces by Simon Donaldson, Oxford Graduate Texts in Mathematics, 22, Oxford University Press, 2013

• Preparation requirements: active knowledge of basic analysis and in particular complex analysis; some knowledge of manifolds and differential geometry.

• Instructor: Viktor Ginzburg; office: McHenry 4124
  email: ginzburg(at)ucsc.edu, phone: 459-2218

• Office Hours: Tu 12:00-1:00pm, Th 1:00-2:00pm or by appointment

• Tentative Syllabus: Riemann surfaces are among the most important objects in mathematics. They are ubiquitous and arise in virtually all fields of mathematics and many areas for mathematical physics from analysis and complex analysis to differential equations to number theory and Galois theory to algebraic and differential geometry to string theory and mirror symmetry. One cannot imagine modern mathematics without Riemann surfaces. In fact, one could probably argue that the theory of Riemann surfaces is one of the starting points of modern math.

  In this course, moving at a relaxed pace, we will cover the basics of Riemann surfaces: examples, constructions, the origins, basic properties, connections with topology of surfaces. If time permits we will look into some deeper results such as the uniformization theorem and the Riemann-Roch theorem.

  In contrast with my other courses, this time I will closely follow the textbook, which by the way I strongly recommend. This is a very nice, well written book, and I will frequently refer to it in class. As in many other advanced, topics courses there will be no exams.