The conference venue and program
Professor Terence Tao will give a public lecture on Wednesday, September 6 at 17:00. The lecture will take place in Lecture Theater IICDEF at the Faculty of Chemistry of the University of Wroclaw, F. Joliot-Curie 14, 50-383 Wroc│aw. This is 5-10 minutes by walk from the conference venue (the place is marked by P on the map below). There is no registration for the participants of the conference. Details of the talk title and abstract are as follows:
Terence Tao (University of California, Los Angeles)
Title: The Erd§s discrepancy problem.
Abstract: The discrepancy of a sequence \(f(1), f(2), \ldots \) of numbers is defined to be the largest value of \(|f(d) + f(2d) + \ldots + f(nd)|\) as \(n,d\) range over the natural numbers. In the 1930s, Erd\"os 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 Erd§s 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.