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SUMMARY:The sharp threshold for making squares - Paul Balister (University
  of Memphis)
DTSTART:20160211T143000Z
DTEND:20160211T153000Z
UID:TALK63266@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Many of the fastest known algorithms for factoring large integ
 ers rely on finding subsequences of randomly generated sequences of intege
 rs whose product is a perfect square. Motivated by this\, in 1994 Pomeranc
 e posed the problem of determining the threshold of the event that a rando
 m sequence of N integers\, each chosen uniformly from the set {1\,...\,x}\
 , contains a subsequence\, the product of whose elements is a perfect squa
 re. In 1996\, Pomerance gave good bounds on this threshold and also conjec
 tured that it is sharp.\n\nIn a paper published in Annals of Mathematics i
 n 2012\, Croot\, Granville\, Pemantle and Tetali significantly improved th
 ese bounds\, and stated a conjecture as to the location of this sharp thre
 shold. In recent work\, we have confirmed this conjecture. In my talk\, I 
 shall give a brief overview of some of the ideas used in the proof\, which
  relies on techniques from number theory\, combinatorics and stochastic pr
 ocesses. Joint work with Béla Bollobás and Robert Morris.\n
LOCATION:MR12
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