Aim

The aim of this mini-course is to introduce the topic of sum-product phenomena in the area of additive combinatorics. Roughly speaking, given a finite set, we consider its sum-set and product-set. A basic question is what we can say about the size of these two sets compared with the original given set. It turns out this basic question attracts three famous mathematicians, Bourgain, Katz and Tao, to give a complete answer. Our goal is to study the work of Bourgain-Katz-Tao on their sum-product results, and discuss its applications on other famous problems in discrete geometry such as Erdos distance problem and Kakeya problem. Students who know how add and multiply two numbers are completely qualified to attend this course. 

Time

Lectures :  10 am to 12pm on 6/26 (Mon), 6/28 (Wed), 6/30 (Fri), 7/3 (Mon), 7/5 (Wed)

Discussions: 1:30 pm to 2:30 pm on 7/3(Mon) and 7/5 (Wed)

Registration

https://goo.gl/forms/DvlUc9nMOyPcbtiM2