| Abstract: | Sieve methods have been used for more than a century to
extract information about the distribution of prime numbers. There are
now many variants available, and recent years have seen striking
successes and developments of sieve principles, sometimes in surprising
areas. The lectures will give a survey of some of the techniques and
results, emphasizing the recent and more surprising applications (for
instance, sieving in the context of discrete groups, the work of
Holowinsky and Soundararajan on Arithmetic Quantum Unique Ergodicity, and
that of Goldston, Pintz and Yildirim on gaps between primes) |