BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:On a conjecture of Serre - Lillian Pierce (Oxford)
DTSTART:20130508T150000Z
DTEND:20130508T160000Z
UID:TALK44007@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:A conjecture of Serre concerns the number of rational points o
 f\nbounded height on a finite cover of projective space. This talk will de
 scribe\njoint work with Roger Heath-Brown that verifies Serre's conjecture
  in certain\nspecial cases\, and even improves on it in sufficiently high 
 dimensions. The\nproblem boils down to giving a good upper bound for the n
 umber of perfect power\nvalues of a polynomial in many variables with inte
 ger coefficients. Such an\nupper bound is obtained via a combination of te
 chniques in analytic number\ntheory\; we will highlight the power sieve\, 
 the q-analogue of van der Corput's\nmethod\, and an arithmetic version of 
 Poisson summation.
LOCATION:MR4\, CMS
END:VEVENT
END:VCALENDAR