Terence Tao (UCLA, USA), Erdős discrepancy problem

Oddział Wrocławski
śr, 2017-09-06 17:00

Oddział Wrocławski PTM i organizatorzy konferencji Analysis and Applications, Wrocław 2017

zapraszają na otwarty wykład laureata Medalu Fieldsa (2006)

Terence’a Tao (University of California, Los Angeles, USA)


Erdős discrepancy problem,

który odbędzie się w dniu 6 września 2017 roku (środa) w sali IICDEF Wydziału Chemii Uniwersytetu Wrocławskiego, przy ul. Fryderyka Joliot-Curie 14. Początek wykładu o godzinie 17:00.

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. 

                                                                                                                                                                                                                                                 Terence Tao