sem set estimates and analytic methods

[Liu]

There are this time two sub plans for me to cover.
Sub plan on general Sum set estimates

Chapter two of the book “Additive Combinatorics” is an introduction to
sum set estimates. Long arithmetic progression is only one aspect of
the whole picture. (It is a major one, of course) I will cover the
eight sections carefully except section 2.7 “Non-commutative analogs”.

Sub plan on finite Fourier Analytic methods

Finite Fourier analysis provides people with a powerful tool to deal
with Additive Combinatorics problems. It can divide additive sets into
two classes, namely Pseudo-random sets and almost periodic sets, the
later including long arithmetic progressions. This dichotomy between
randomness and structure is also the emphasis of Terence Tao’s Ergodic
Theory lecture notes online. The deep link between Ergodic Theory and
Additive Combinatorics is my main interest.