On the sum-product problem

Series
Job Candidate Talk
Time
Tuesday, February 15, 2022 - 11:00am for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
George Shakan – CRM – george.shakan@gmail.com – https://gshakan.wordpress.com/about-the-blogger/
Organizer
Benjamin Jaye

Let A be a subset of the integers of size n. In 1983, Erdos and Szemeredi conjectured that either A+A or A*A must have size nearly n^2. We discuss ideas towards this conjecture, such as an older connection to incidence geometry as well as somewhat newer breakthroughs in additive combinatorics. We further highlight applications of the sum-product phenomenon.