Terence Tao: The Erdős Discrepancy Problem
UCLA Mathematics Colloquium
"The Erdős Discrepancy Problem"
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, 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 this September. In this talk I will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.
Institute for Pure and Applied Mathematics, UCLA
October 8, 2015
For more information: http://www.ipam.ucla.edu/news/terry-tao-proves-erdos-discrepancy-problem/#:~:text=In%20the%201930s%2C%20Hungarian%20mathematician,matter%20the%20sequence%20you%20choose.
Видео Terence Tao: The Erdős Discrepancy Problem канала Institute for Pure & Applied Mathematics (IPAM)
"The Erdős Discrepancy Problem"
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, 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 this September. In this talk I will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.
Institute for Pure and Applied Mathematics, UCLA
October 8, 2015
For more information: http://www.ipam.ucla.edu/news/terry-tao-proves-erdos-discrepancy-problem/#:~:text=In%20the%201930s%2C%20Hungarian%20mathematician,matter%20the%20sequence%20you%20choose.
Видео Terence Tao: The Erdős Discrepancy Problem канала Institute for Pure & Applied Mathematics (IPAM)
Показать
Комментарии отсутствуют
Информация о видео
10 октября 2015 г. 4:17:21
00:51:49
Другие видео канала
The World's Best Mathematician (*) - NumberphileTerence Tao's Analysis I and Analysis II Book ReviewtaoFour Minutes With Terence TaoBreakthrough Prize in Mathematics 2014The Heidelberg Laureate Forum Foundation presents the HLF Portraits: Terence TaoTerry Tao, Ph.D. Small and Large Gaps Between the Primes2015 Math Panel with Donaldson, Kontsevich, Lurie, Tao, Taylor, MilnerThe Most Beautiful Equation in MathTerence Tao: The Cosmic Distance Ladder, UCLAWhy the World’s Best Mathematicians Are Hoarding ChalkTerence Tao: An integration approach to the Toeplitz square peg problemThe Test That Terence Tao Aced at Age 7An Interview with Terence TaoRIA Hamilton Lecture 2020 - Professor Terence TaoMath gold medalist talks about the art of mathMath Prodigy Terence Tao, UCLAPulling back the curtain: Terence Tao on mathematics in the Internet ageAdvanced Algorithms (COMPSCI 224), Lecture 1