2:00 - 3:30 p.m.
Several complex variables (First lecture)
Gautam Bharali
IISc., Bangalore.
26-09-11 (Set of lectures)

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Abstract

Some of earliest classical results in the theory of functions in several complex variables, that established it as a field quite distinct from univariate complex analysis, deal with the fact that there exist domains such that all complex-analytic functions on them extend analytically to strictly larger domains. In this series of talks, we shall try to understand the above phenomenon, and to characterize those domains that are the true domains of definition of all the functions holomorphic on them. This effort led to the invention of several concepts that are indigeneous to several complex variables -- most notably those of plurisubharmonicity and pseudo-convexity. We shall examine where these objects originate from, and why they are needed.