||A way to describe our talk is how to borrow ideas from commutative algebra to
study Hilbert spaces and their operators. When the Hilbert spaces consist of analytic
functions, complex analysis comes into play.
The main concepts involved in this talk: functional analysis includes Fredholm index and
operators on function spaces; commutative algebra is mainly about Hilbert polynomial,
Samuel multiplicity, and Koszul complex; complex analysis concerns analytic functions on
the unit disk in the complex plane.