Terence Tao (YouTube)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 and 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 Radziwiłł, as well as a surprising application of the Shannon entropy inequalities, the Erdős discrepancy problem was solved in 2015. In his talk TT will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.
