Montreal Number Theory webpage
(including QuebecVermont seminar, and analytic number theory seminar)
Useful references
Number theory journals

We are sieving a set of size X (perhaps the integers in an interval) with the primes for a given set P. The "probability" that a given element of our set is divisible by p, from P, is about 1/p. In order to use some sort of inclusionexclusion argument, we will need to know the "probability" that a given element of our set is divisible by pq, with p,q from P. We expect this to be 1/pq, but if pq>X then this will have to rather inaccurate. So the many wonderful results of sieve theory typically work under the assumption the primes in P are less than X^(1/2).
But what if we allow some of the primes in P to be greater than X^(1/2) ? We know many examples where the number of integers left unsieved is far less than one might guess, in this case. In this article Dimitris Koukoulopoulos, Kaisa Matomaki and I show that there exists a constant k>1 such that if we are sieving the interval [1,X], and the sum of the reciprocals of the primes up to X that are not in P, is >k, then the number of integers left unsieved is roughly as one might guess. Moreover we conjecture that one can take any k>1, and speculate that an analogous result may be true when sieving any interval.
The proof revolves around a quantative estimate for additive combinatorics for sumsets.
Don't be seduced by the zeros!
Different approaches to the distribution of primes
The Princeton Companion to Mathematics: Analytic number theory
Prime number patterns (2009 Ford Prize)
It is easy to determine whether a given integer is prime (2008 Chauvenet Prize)
Prime number races (2007 Ford Prize)
It's as easy as abc
Zaphod Beeblebrox's brain and the fiftyninth row of Pascal's triangle (1995 Hasse Prize)

Mar 2830, 2014: Yale math morning and colloquium
Apr 26, 2014: MSRI Math Lovers forum
May 2930, 2014: Number fields and function fields, Royal Society, Chicheley Hall, Bucks
June 23July 4, 2014: Summer school on Counting Arithmetic Objects, CRM, Montreal
July 925, 2014: Summer School on Analytic Number Theory, IHES, Paris
Sept 1519, 2014: Statistics and number theory, CRM, Montreal
Sept 2226, 2014: LMSCMI Research school on Bounded Gaps Between Primes, Oxford
Sept 29Oct 3, 2014: CMI workshop, Analytic number theory, Oxford
Oct 610, 2104: Additive Combinatorics and expanders, CRM, Montreal
Nov 1014, 2014: Counting arithmetic objects, CRM, Montreal
Dec 812, 2014: Probabilistic and multiplicative number theory, CRM Montreal
Need a reference?
Public lectures
