In his seminal work from 1979,
Joseph J. Kohn invented
his theory of multiplier ideal sheaves
connecting a priori estimates for the d-bar problem
with local boundary invariants
constructed in purely algebraic way.
I will explain the origin and motivation of the problem,
and how Kohn's algorithm reduces it
to a problem in local geometry
of the boundary of a domain.
I then present my recent work with Sung Yeon Kim
based on the technique of jet vanishing orders,
and show how it can be used to
control the effectivity of multipliers in Kohn's algorithm,
subsequently leading to precise a priori estimates.