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BEGIN:VEVENT
DTSTAMP:20220207T120213Z
DTSTART:20220222T150000Z
DTEND:20220222T160000Z
SUMMARY:Natalie Evans (King's College London)  - Correlations of almost p
 rimes
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}u144-kz1e4n
 or-5hrrz8
DESCRIPTION:Abstract : The Hardy-Littlewood generalised twin prime conjec
 ture states an asymptotic formula for the number of primes $p\\le X$ suc
 h that $p+h$ is prime for any non-zero even integer $h$. While this conj
 ecture remains wide open\, Matom\\"{a}ki\, Radziwi{\\l}{\\l} and Tao pro
 ved that it holds on average over $h$\, improving on a previous result o
 f Mikawa. In this talk we will discuss an almost prime analogue of the H
 ardy-Littlewood conjecture for which we can go beyond what is known for 
 primes. We will describe some recent work in which we prove an asymptoti
 c formula for the number of almost primes $n=p_1p_2 \\le X$ such that $n
 +h$ has exactly two prime factors which holds for a very short average o
 ver $h$.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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