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Multivariable Complex Analysis

Dates and times

Lecture

Tuesday, 16:15-17:45, HS 3, Building E 2 5

Tutorial

Wednesday, 14:15-15:45, SR 5, Building E 2 4

You may submit the solutions for the assignments in teams of up to three people.

Contents

This course is an introduction to complex analysis in several variables. While many of the basic results about holomorphic functions of one variable carry over to several variables, a number of new phenomena arise. For instance, holomorphic functions of several variables cannot have isolated zeros or isolated singularities.

Topics covered:

  • basic properties of holomorphic functions of several variables
  • Hartogs' theorem about seperately holomorphic functions
  • analytic sets
  • domains of holomorphy

Prerequisites

Basic complex analysis in one variable (e.g. Funktionentheorie 1).

Exam

There will be an oral exam at the end of the semester. In order to be eligible for the exam, you have to achieve at least 50% of the available points on the assignments.

Literature

See here

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