We will begin with a brief overview of when holomorphic functions of 
more than one complex variable extend to a larger domain (Hartogs' Theorem and 
Pseudoconvexity). We then proceed to discuss a recent result which shows that, 
on a class of domains with circular symmetries, the Bergman projection of 
conjugate holomorphic functions (also called the Friedrichs operator) extend 
holomorphically to a larger domain. The Bergman projection, on a domain 
$\Omega$, is the orthogonal projection from $L^2(\Omega)$ onto 
$L^2(\Omega)\cap\{\text{holomorphic functions in } \Omega\}$. We will use 
simple examples and geometric reasoning throughout the presentation. This is 
joint work with Yunus Zeytuncu.