Lectures
Wednesday 10-10:55
Thursday 10-10:55
Summaries of lectures are available here.
Homework problems
Weekly homework problems will be uploaded here.
Course contents
Holomorphic functions, Cauchy’s integral formula and consequences, open mapping theorem, Weierstrass and Montel’s theorem, power series and Reinhardt domains, domains of holomorphy, pseudoconvexity and plurisubharmonicity. Analytic sets, Rieman’s continuation theorem, Rado’s theorem, Hartogs' continuation theorem. Automorphisms of circular domains, Cartan’s theorem, Poincare’s theorem.
Textbook
R. Michael Range, Holomorphic functions and integral representations in several complex variables
References
1. Lars Hormander, An introduction to complex analysis in several variables
2. Steven G. Krantz, Function theory of several complex variables
3. Raghavan Narasimhan, Several complex variables
4. B. V. Shabat, Introduction to complex analysis. Part II. Functions of several complex variables
Suggested Readings
1. Debraj Chakrabarti, Several complex variables are better than just one. Resonance (2011)
2. Steven G. Krantz, What is several complex variables? Amer. Math. Monthly (1987), 236–256.
3. R. Michael Range, Complex analysis: a brief tour into higher dimensions. Amer. Math. Monthly (2003), 89–108.
Evaluation
Mid-sem 30%
End-sem 30%
Quizzes, Assignments, Presentations 40%