# Geometry of real hypersurfaces meets Subelliptic PDEs

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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.