My university offers $3$ complex analysis courses:
- an introduction computational course
- Chapters $1$ - $5$ of Ahlfors
- a course covering compactness and convergence in the space of analytic functions, Riemann mapping theorem, Weierstrass factorization theorem, Runge's theorem, Mittag-Leffler theorem, analytic continuation and Riemann surfaces, and Picard theorems
I plan to take these three in the next few years. However, I am curious about complex analysis and would like to continue my studies after the introductory level. Which area(s) of complex analysis are worth studying currently i.e. several complex variables, operator theory, or differential equations? Which texts should I pursue after Ahlfors? I am studying physics also, so a text with rigorous results in quantum mechanics or other related fields would be nice :)
Thanks in advance for advice!