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Level: BSc, MSci, MSc
Title: Sieve methods
Supervisor:

Dr Steve Lester
Research Area: Algebra
Description:

The Twin Prime Conjecture asserts that there are infinitely many primes p such that p+2 is also prime. This conjecture is still open, but there has been spectacular progress on this problem recently using sieve methods. The aim of this project is to learn sieve methods and study how these techniques are applied to problems about prime numbers such as the Twin Prime Conjecture, or, primes of the form n^2+1.
Further Reading:
  • H. Iwaniec, J. Friedlander, Opera de Cribro. Colloquium Publications, Vol. 57, American Mathematical Society, 2010.
  • H. Halberstam, H.-E. Richert, Sieve Methods. Academic Press, London, 1974.
  • H. Iwaniec, E. Kowalski, Analytic Number Theory. Colloquium Publications, Vol. 53, American Mathematical Society, 2004.
  • J. Maynard, Small gaps between primes, Annals of Mathematics 181 (2015) 383–413.
Key Modules:

MTH5103 Complex Variables (desirable)

MTH6109 Combinatorics (desirable)

Other Information:

Knowledge of harmonic analysis,  complex analysis, and combinatorics would be useful but not necessary.
Current Availability: Yes