The general theory of holomorphic mappings between bounded domains, automorphisms of bounded
domains, discussions on the non-existence of a classical Riemann Mapping Theorem in several
variables, discussion of the various forms of the one-variable Riemann Mapping Theorem, the
Rosay-Wong Theorem, other Riemann-Rosay-Wong-type results (e.g., the work of Pinchuk) to the
extent that time permits.

Suggested books and references:

Krantz, S. G., Geometric analysis and function spaces, CBMS Regional Conference Series in Mathematics, 81 (A M S, Providence, USA).

Rudin, W., Function theory in the unit ball of $\mathbb{C^n}$, Grundlehren der Mathematischen Wissenschaften (Springer-Verlag, New York-Berlin, 1980).

Krantz., S. G., Function theory of several complex variables, AMS Chelsea Publishing, Providence, RI, 2001.