Speaker  : Terence Tao (UCLA)


Date  : June 28, 2017
Time  : 17:00  - 18:00
Place : Room 1114, KIAS, Seoul

Title  : The Erdős discrepancy problem

Abstract
The discrepancy of a sequence f(1), f(2), ... of numbers is defined to be the largest value of |f(d) + f(2d) + ... + f(nd)| as n,d range over the natural numbers. In the 1930s, Erdos posed the question of whether any sequence consisting only of +1 and -1 could have bounded discrepancy. In 2010, the collaborative Polymath5 project showed (among other things) that the problem could be effectively reduced to a problem involving completely multiplicative sequences. Finally, using recent breakthroughs in the asymptotics of completely multiplicative sequences by Matomaki and Radziwill, as well as a surprising application of the Shannon entropy inequalities, the Erdos discrepancy problem was solved in 2015. In this talk I will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.



Organizer
Jaigyoung Choe (KIAS)

Contact
Kangwon Lee (KIAS)
(kwlee@kias.re.kr, +82-2-958-3774)