Meromorphic Functions on the Riemann Sphere

What it is about

You deal with meromorphic functions on the Riemann sphere, with covering mappings and Möbius transformations as well as with elliptic functions and their topology. In the end you will be able to construct meromorphic continuations, specify coverings and you will know the fundamentals of Riemann surfaces.

What you will be able to do

• Understand the concept of a meromorphic function on the Riemann sphere
• Construct covering mappings
• Apply Möbius transformations
• Investigate the properties of singly and doubly periodic functions
• Describe elliptic functions and their topology
• Produce meromorphic continuations
• Understand fundamental concepts of Riemann surfaces

What the module consists of

• VorlesungDelivery of the content through lectures, examples and discussion for introduction and motivation
• ÜbungProblem sets with solutions for self-check and deepening understanding

Teaching method

• Vorlesungto present the theory with illustrative examples and to motivate independent engagement
• Übungto deepen understanding through problem sets and solution checking