[2017 CMC Distinguished Lecture Series by Terence Tao]

** Date: ** 2017-06-15

**Speaker :** Terence Tao (UCLA)

**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.

**VOD : **[Android_VOD] [iPhone_VOD] [Windows_VOD]

Information Center for Mathematical Sciences KAIST

305-701 대전광역시 유성구 대학로 291 (구성동373-1)

한국과학기술원(KAIST) 수리과학정보센터

전화 042-350-8195~6 / 팩스 042-350-5722

e-mail : mathnet@mathnet.or.kr

Copyright (C) 2017. ICMS All Rights Reserved.

305-701 대전광역시 유성구 대학로 291 (구성동373-1)

한국과학기술원(KAIST) 수리과학정보센터

전화 042-350-8195~6 / 팩스 042-350-5722

e-mail : mathnet@mathnet.or.kr

Copyright (C) 2017. ICMS All Rights Reserved.