The Selberg Sieve and Large Sieve - Lecture 1

Explore the foundations of additive combinatorics in this lecture on The Selberg Sieve and Large Sieve. Delve into key concepts including linear algebra, propositions, and the duality principle. Learn about the Bombieri-Vinogradov theorem and gain insights into the general philosophy behind sieve methods. Examine proofs, corollaries, and practical examples to deepen your understanding of these advanced mathematical techniques. Ideal for researchers and students in number theory and combinatorics, this comprehensive talk provides a solid foundation for further study in the field.

The Selberg Sieve and Large Sieve
Plan
Some Linear Algebra
Proposition
Proof
Q: How small can Delta be?
Proposition Duality Principle
Remark
Proof
Corollary
Duality Principle
Theorem 0:
Proof
Remark
General Philosophy
Example - Bombier-Vinogrador theorem