Topics in complex analysis

Summary

The goal of this course is to treat selected topics in complex analysis. We will mostly focus on holomorphic functions in one variable. At the end we will also discuss holomorphic functions in several variables

Content

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Keywords

Complex analysis, Mittag-Leffler theorem, Weierstrass product theorem, Riemann mapping theorem, Picard's great theorem, several complex variables

Learning Prerequisites

Required courses

Analysis I-III (especially basic theory of holomorphic functions)

Important concepts to start the course

Basic theory of holomorphic functions in one complex variable

Learning Outcomes

By the end of the course, the student must be able to:

• Understand the concepts and methods taught in the course and during the exercise classes
• Apply those concepts and methods to analyze and solve problems in complex analysis

Teaching methods

Lectures with beamer presentation of the script and blackboard (for proofs, sketches, images, and interactive discussions). Exercise sessions with assistant

Expected student activities

Attending the lectures, solving the exercises

Assessment methods

Written exam

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours	Yes
Assistants	Yes
Forum	Yes
Others	Office hours by appointment

Resources

Bibliography

R. Remmert. Classical topics in complex function theory. Springer, New York, 1998

C. Laurent-Thiébaut. Holomorphic function theory in several variables: an introduction, Springer, London, 2011

Ressources en bibliothèque

• Classical topics in complex function theory / Remmert
• Holomorphic function theory in several variables / Laurent-Thiébaut

Notes/Handbook

There will be lecture notes available in Moodle

Moodle Link

• https://go.epfl.ch/MATH-327