MATH 5121: Topics in Complex Function Theory
Description: Advanced topics of contemporary interest. These include Riemann surfaces, Kleinian groups, entire functions, conformal mapping, several complex variables, and automorphic functions, among others. With a change of content this course may be repeatable to a maximum of twelve credits.
Prerequisites: MATH 5120.
MATH 5121 - Section 1: Riemann surfaces and complex geometry
Description: A Riemann surface is a two-dimensional real manifold from a topological point of view. From the viewpoint of complex geometry, it is a one-dimensional complex (Kahler) manifold. In algebraic geometry a Riemann surface is a smooth complex algebraic curve. A Riemann surface can also be viewed as an algebraic function field of one variable over the complex numbers. We shall develop tools to study three main topics: the Hodge Theorem, Kodaira's vanishing and embedding theorem, and Yau's resolution of the Calabi conjecture. The main tools are partial differential equations and sheaf cohomology. We shall discuss various applications to differential geometry, topology, and algebraic geometry. Normally the techniques and concepts that look difficult and abstract in higher dimensions can be seen and understood clearly in the case of Riemann surfaces.
Sections: Fall 2016 on Storrs Campus
|07699||5121||001||Lecture||TuTh 12:30:00 PM-01:45:00 PM||MONT 421||Wu, Damin|