Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The prototypical example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the prototypical example of a sieve is the sieve of Eratosthenes, or the more general Legendre sieve. The direct attack on prime numbers using these methods soon reaches apparently insuperable obstacles, in the way of the accumulation of error terms. In one of the major strands of number theory in the twentieth century, ways were found of avoiding some of the difficulties of a frontal attack with a naive idea of what sieving should be. One successful approach is to approximate a specific sifted set of numbers (e.g. the set ofprime numbers) by another, simpler set (e.g. the set of almost prime numbers), which is typically somewhat larger than the original set, and easier to analyze. More sophisticated sieves also do not work directly with sets per se, but instead count them according to carefully chosen weight functions on these sets (options for giving some elements of these sets more "weight" than others). Furthermore, in some modern applications, sieves are used not to estimate the size of a siftedset, but to produce a function that is large on the set and mostly small outside it, while being easier to analyze thanthe characteristic function of the set. (Wikipedia).
Group theoretic applications of the large sieve method - Chen Meiri
Speaker: Chen Meiri (Technion) Title: Group theoretic applications of the large sieve method Abstract: In this talked we will explain how the classical large sieve method from number theory can be applied to study properties of subsets of groups which have property-τ . As an application we
From playlist Mathematics
Sieve methods: what are they, and what are they good for? - James Maynard
Analysis Seminar Topic: Sieve methods: what are they, and what are they good for? Speaker: James Maynard Affiliation: Member, School of Mathematics Date: December 13, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
The Nature of Causation: The Counterfactual Theory of Causation
In this second lecture in this series on the nature of causation, Marianne Talbot discusses the counterfactual theory of causation. We have causal theories of reference, perception, knowledge, content and numerous other things. If it were to turn out that causation doesn’t exist, we would
From playlist The Nature of Causation
Sieve Of Eratosthenes (visualized)
This is a visualization of the Sieve of Eratosthenes used to find the primes up to 900. We only need to check for divisibility by primes up to 30, which is the square root of 900 so we find these primes relatively quickly. #manim #sieve #eratosthenes #visualmath #math #mtbos #primes #numbe
From playlist Number Theory
Is the Sieve of Eratosthenese past its prime?
The Sieve of Eratosthenes is an amazing tool for teaching people about prime numbers and composite numbers but it's not without its limitations. I've tried to answer the question, 'Is there a better way of representing a sieve like this?' 0:00 Sieve of Eratosthenes In the first part of t
From playlist Summer of Math Exposition Youtube Videos
This lecture is part of an online course on Galois theory. This is an introductory lecture, giving an informal overview of Galois theory. We discuss some historical examples of problems that it was used to solve, such as the Abel-Ruffini theorem that degree 5 polynomials cannot in genera
From playlist Galois theory
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Combinatorial affine sieve - Alireza Salehi Golsefidy
Speaker: Alireza Salehi Golsefidy (UCSD) Title: Combinatorial affine sieve Abstract: In this talk the general setting of affine sieve will be presented. Next I will explain the Bourgain-Gamburd-Sarnak method on proving affine sieve in the presence of certain spectral gap. Finally I will sa
From playlist Mathematics
Davide Gabrielli : Macroscopic fluctuation theory / Macroscopic fluctuation theory
Abstract: In this second lecture I will discuss the basic ideas of the macroscopic fluctuation theory as an effective theory in non equilibrium statistical mechanics. All the theory develops starting from a principal formula that describes the distribution at large deviations scale of the
From playlist Mathematical Physics
Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
John Friedlander - Selberg and the sieve: a positive approach [2008]
The Mathematical Interests of Peter Borwein: "Selberg and the sieve: a positive approach" Date: Friday, May 16, 2008 Time: 09:00 - 10:15 Location: Rm10900 John Friedlander (University of Toronto) Abstract: We survey the contributions of Atle Selberg to Sieve Methods. The talk is intende
From playlist Number Theory
Primality test with sieve | Journey into cryptography | Computer Science | Khan Academy
An attempt at an optimal trial division primality test using the Sieve of Eratosthenes. Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/comp-number-theory/v/prime-number-theorem-the-density-of-primes?utm_source=YT&utm_medium=Desc&utm_campaign=com
From playlist Journey into cryptography | Computer Science | Khan Academy
The Selberg Sieve and Large Sieve (Lecture 4) by Satadal Ganguly
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, ergod
From playlist Workshop on Additive Combinatorics 2020
Gaps between Primes (extra footage) - Numberphile
More links & stuff in full description below ↓↓↓ Main video at: http://youtu.be/vkMXdShDdtY Brown papers available: http://bit.ly/brownpapers Prime number playlist: http://bit.ly/11kSUmF Featuring Ed Copeland and Tony Padilla (with a very non-expert intro by Brady). NUMBERPHILE Website:
From playlist Numberphile Videos
CTNT 2020 - Sieves (by Brandon Alberts) - Lecture 3
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Sieves (by Brandon Alberts)
Jason Parker - Covariant Isotropy of Grothendieck Toposes
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/ParkerSlidesToposesOnline.pdf Covariant isotropy can be regarded as providing an abstract notion of conjugation or i
From playlist Toposes online
CTNT 2020 - Sieves (by Brandon Alberts) - Lecture 5
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Sieves (by Brandon Alberts)
CTNT 2020 - Sieves (by Brandon Alberts) - Lecture 1
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Sieves (by Brandon Alberts)
Laurent Lafforgue - 1/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Courses - G. JONA LASINIO “Macroscopic Fluctuation Theory”
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics approach, these states have been the subject of several th
From playlist T1-2015 : Disordered systems, random spatial processes and some applications