Abstract: The space of all square integrable holomorphic functions on a domain in the complex plane was first systematically studied by Bergman in the 1920s. Since that time, the program to study these spaces, called Bergman spaces, has expanded to interact with many areas of complex analysis, operator theory, complex geometry and algebraic geometry. The most recent addition to the program involves studying how these Bergman spaces change when the structures defining these spaces are deformed. In this talk I will discuss my some of the major results in the area, and a new contribution I have made to it.

https://www.math.stonybrook.edu/cards/varolindror.html