Explore Kähler-Einstein Bergman metrics on pseudoconvex domains in this 43-minute conference talk from the Workshop on "Analysis and Geometry in Several Complex Variables" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into Yau's conjecture asserting that the Bergman metric on a bounded pseudoconvex domain in C^n is Kähler-Einstein if and only if the domain is homogeneous. Examine Cheng's special case of this conjecture regarding smoothly bounded strongly pseudoconvex domains. Discover old and new results concerning these conjectures and investigate related questions in the field of complex geometry.