I have a friend who is a professor with a PhD in complex analysis. Multivariable complex analysis (along with the theories of complex manifolds and analytic spa

I have a friend who is a professor with a PhD in complex analysis. Multivariable complex analysis (along with the theories of complex manifolds and analytic spaces) is very far from over. Heck, one of the Millennium Problems (the Hodge conjecture) is in complex geometry (granted, in the more algebraically flavoured part of it).