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250064 VO Advanced complex analysis (2020W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Monday 05.10. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 06.10. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 12.10. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 13.10. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 19.10. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 20.10. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 22.10. 15:00 - 16:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 27.10. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 03.11. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 09.11. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 10.11. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 16.11. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 17.11. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 23.11. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 24.11. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 30.11. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 01.12. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 07.12. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 14.12. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 15.12. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 11.01. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 12.01. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 18.01. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 19.01. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 25.01. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 26.01. 16:45 - 17:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This is the continuation of the standard complex analysis course. After revising briefly the residue theorem and other classical theorems we will address classical results in one variable, especially the Riemann mapping theorem, Rouché's theorem, the characterization of the automorphism groups of complex domains, Runge's theorem, etc. We will then proceed to holomorphic functions in several variables and prove Hartogs theorem, the Weierstrass preparation theorem, the Riemann extension theorem and several other results. If time permits we will treat also complex manifolds, sheaf theory and the famous Oka coherence theorems.

Assessment and permitted materials

Oral exam (in some cases, also a write-up of further topics may replace the exam)

Minimum requirements and assessment criteria

The students are encouraged to have a recap of their basic complex analysis class to be well prepared at the beginning of the semester. We will assume that the respective material is well understood and present. To this end, Remmert's Complex Analysis (can be found on the web) maybe helpful.

Examination topics

Reading list

Remmert: Funktionentheorie / Complex Functions
Freitag-Lieb: Funktionentheorie
Ahlfors: Complex Analysis
Jänich: Funktionentheorie
Cartan: Analytische Funktionen
Rainer: Complex Analysis

Association in the course directory

MANK

Last modified: Mo 22.02.2021 10:29