(FYI: 2017 CMC Distinguished Lecture Series)
The Erdős discrepancy problem
Terence Tao
Department of Mathematics, UCLA
Department of Mathematics, UCLA
2017/06/15 4PM (Fusion Hall, KI Bldg.)
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, Erdős 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 Erdős 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.