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SUMMARY:Primes in arithmetic progressions to smooth moduli - Julia Stadlma
 nn (Oxford)
DTSTART:20240213T143000Z
DTEND:20240213T153000Z
UID:TALK210547@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION:The twin prime conjecture asserts that there are infinitely ma
 ny primes p for which p+2 is also prime. This conjecture appears far out o
 f reach of current mathematical techniques. However\, in 2013 Zhang achiev
 ed a breakthrough\, showing that there exists some positive integer h for 
 which p and p+h are both prime infinitely often. Equidistribution estimate
 s for primes in arithmetic progressions to smooth moduli were a key ingred
 ient of his work. In this talk\, I will sketch what role these estimates p
 lay in proofs of bounded gaps between primes. I will also show how a refin
 ement of the q-van der Corput method can be used to improve on equidistrib
 ution estimates of the Polymath project for primes in APs to smooth moduli
 .
LOCATION:MR13
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