# Geometric ideas in Sum-Product theory

## Abdul Basit, Rutgers University

## March 21, 2017

The sum-product conjecture of Erdos-Szemeredi states that
for any finite set $A$ of the reals $$\max(|A+A|, |AA|) \geq |A|^{2 -
\varepsilon}.$$ Here $A+A$ (resp. $AA$) is the set of all pairwise sums (resp.
products) of elements of $A$. We will go over some sum-product type
estimates and see how ideas from geometry come into play when proving
such estimates.