C O L L O Q U I U M

 

Selberg's -sieve

 

Dr. Kai Man Tsang

The University of Hong Kong

 

Abstract

Selberg's L2-sieve is a neat and versatile tool in analytic number theory.  Its main idea originates from Selberg's work on the theory of the Riemann zeta-function back in the 1940's. Earlier applications of the L2-sieve include approximations to the Goldbach and prime twins problems.

Since 2004, there are two extraordinary breakthroughs in the theory of the primes, namely, the Green-Tao theorem on arbitrarily long arithmetic progressions of primes, and the Goldston-Pintz-Yildirim theorems on small gaps between primes. Selberg's L2-sieve played a central role in both of these. 

In these two talks, I will first introduce the L2-sieve and describe some of its earlier applications. Then I will discuss some more recent results and describe the action of the L2-sieve in the above-mentioned breakthroughs in the distribution of the primes.

 

Lecture 1:

March 3, 2006   (Friday)

4:00 – 5:00pm

Lecture 2:

March 10, 2006 (Friday)

4:00 – 5:00pm

 

Lectures will be held in Room 517, Meng Wah Complex, HKU

Tea will be held in Room 516, Meng Wah Complex at 3:40pm

 

All are welcome