Analysis of Boolean Functions and (a small sample of) Applications

Representing a Boolean function as a polynomial is only natural. It
turns out that this representation, along with some related techniques
-- for example the study of the Influence of variables on Boolean
functions -- gives insight to many aspects of such functions. This field
was founded in a paper by Kahn, Kalai and Linial from the end of the
80's, and has since shown applications in a wide array of fields,
including Game Theory and Social Choice, Economics, Percolation, and
Complexity theory.

The talk will survey the methodology and some of its applications, to
Percolation, Mechanism Design, Graph Properties and Complexity Theory.
We would then consider some further applications, show the state of art
in terms of known results in the field; and suggest open problems with
their relevant applications.