Abstract: After learning single-variable calculus, it is common to move straight into learning multivariable calculus; a standard extension from R to R^n. With some dedication, one continues on to learn about single-variable complex analysis, observing that the reasonable transition from R to C often makes analysis much more elegant. But then a natural question arises: Why is it uncommon to study "multivariable complex analysis" on C^n?

In this talk, which shares its title with a textbook authored by Jiří Lebl, we will introduce basic results and phenomena in the theory of several complex variables. Emphasizing definitions and examples over technical proofs, we will explore generalizations of certain theorems from complex analysis, while highlighting the surprising ways in which our single-variable intuition can fail in higher dimensions. Familiarity (not proficiency) in complex analysis will be helpful, but certain statements will be reviewed as needed.