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Lyosha Klurman: "Pretentiousness" in analytic number theory

Tid: On 2017-11-08 kl 13.15

Plats: F11

Medverkande: Lyosha Klurman, KTH

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Since Riemann's groundbreaking 1859 memoir, the study of the distribution
of prime numbers has been dominated by the study of the zeros of the
Riemann zeta function. Over 150 years, various researchers have developed
"ad hoc" approaches to specific questions that did not use Riemann's ideas
directly, yet it was only a few years ago when Andrew Granville and Kannan
Soundararajan suggested that the whole subject might be approached by
coherent alternative ideas based on the concept of "pretentiousness". Using
these ideas, recently, some well-known open questions have been resolved
among which are, the first in 90 years, improvement of the Polya-Vinogradov
inequality (by Granville and Soundararajan), Tao's solution of the Erdos
discrepancy problem, solution of an old conjecture of Erdos and an old
conjecture of Katai about partial sums of multiplicative functions (by the
speaker) and others. In this talk, I will introduce some "pretentious"
ideas and discuss some of their applications.

This is an analysis colloquium style talk.