BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Almost-prime k-tuples - James Maynard (Oxford)
DTSTART:20121121T160000Z
DTEND:20121121T170000Z
UID:TALK39454@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:For $i=1\,\\dots\,k$\, let $L_i(n)=a_i n+b_i$ be linear functi
 ons\nwith integer coefficients\, such that $\\prod_{i=1}^k L_i(n)$ has no 
 fixed\nprime divisor. It is conjectured that there are infinitely many int
 egers\n$n$ for which all of the $L_i(n)$ ($1\\le i \\le k$) are simultaneo
 usly\nprime. Unfortunately we appear unable to prove this\, but weighted s
 ieves\nall us to show that there are infinitely many integers $n$ for whic
 h\n$\\prod_[i=1}^k L_i(n)$ has at most $r_k$ prime factors\, for some\nexp
 licit constant $r_k$ depending only on $k$. We describe new weighted\nsiev
 es which improve these bounds when $k\\ge 3$\, and discuss potential\nappl
 ications to small prime gaps.\n
LOCATION:MR11\, CMS
END:VEVENT
END:VCALENDAR