This course will cover topic in both one and several complex variables. The students are only expected to have a basic course in complex analysis.

We will meet on

• Thurdays from 14:15–16 in room KJL 21
• Friday from 14:15–16 in room KJL 24

The first meeting will be on Thursday 29 August

Books that will be used in the course:

1. "Real and Complex Analysis" W. Rudin
2. "Complex Analysis." Ahlfors
3. "Function Theory in the Unit Ball of C^n." W.Rudin
4. "Lectures on Counterexamples in Several Complex Variables." J.E.Fornæss and B.Stensønes
5. "Several Complex Variables." R.Narasimhan

Suggested Topic for the examination: From the book Lectures on counterexamples in Several Complex Variables. J.E.Fornæss and B.stensønes Lecture 28 Lecture 29 Lecture 30 Lecture 31 Lecture 39 Lecture 47 Lecture 48

Lecture notes

• Week 46
• Automorphisms of \(\mathbb{C}^k\) with an invariant non-recurrent attracting Fatou component biholomorphic to \(\mathbb{C}^k\times (\mathbb{C}^\ast)^{k-1}\) (arXiv)
• Week 42
• Mechthild Behrens -- Plurisubharmonic Defining Functions of Weakly Pseudoconvex Domains in \(\mathbb{C}^2\)
• Stein Olav Romslo -- A Fatou--Bieberbach Domain with a Complex Line in the Boundary
• Rosay and Rudin -- Holomorphic maps from \(\mathbb{C}^n\) to \(\mathbb{C}^n\)
• Week 35

FORELESER ER SYK I DAG 15 NOV. ingen klasse. Remember that this and the next week we only meet on Friday's, i.e. Friday Nov 29 and Friday Dec.6 The exam will be on Tuesday Dec.10 in Realfagsbygget: R Zoo-2 (360.Du2-182)

The exam will be Dec 10 from 10-12 and 13-15 10-12: Aleksei Kulikov, William Tell, Helge Knutsen

13-15: Erlend Bergtun, Tai Nguyen, Knut Bjarne Haus

Berit Stensønes