The Selberg sieve (Lecture 1) by Stephan Baier скачать в хорошем качестве

The Selberg sieve (Lecture 1) by Stephan Baier

Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergodic theory, harmonic analysis and geometry over finite fields. This workshop has been designed to introduce the participants to different facets of additive combinatorics such as the Ramsey theory, inverse problems, polynomial methods, sum-free sets and more. It will also touch upon topics such as the work of B. Green and T. Tao, on long arithmetic progressions in the primes and Sieve methods from number theory. This workshop will appeal to young researchers interested in number theory and combinatorics. It will also be beneficial to researchers working in different areas of mathematics to get an overview of the many different topics in the field of additive combinatorics. CONTACT US: wac20@icts.res.in PROGRAM LINK: https://www.icts.res.in/program/wac20 Table of Contents (powered by https://videoken.com) 0:00:00 The Selberg sieve (Lecture 1) 0:00:52 Introduction 0:11:26 Heuristics about the number of twin primes 0:13:22 Naive heuristics 0:15:04 Hardy - Little Wood 0:19:20 Probability 0:26:24 Goal of the next lectures: Bounds of the forms 0:27:59 Simple Sieve: Sieve of Eratosthenes 0:29:24 Extension Bateman - Horn Conjecture 0:39:27 Goal: detect primes in sequences 0:41:27 Example: n prime 0:54:19 Simple upper bound sieve 0:58:58 Twin primes 1:04:07 By Chinese remainder theorem w(d) is multiplicative