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SUMMARY:Terence Tao (UCLA)
DTSTART:20200414T220000Z
DTEND:20200414T230000Z
DTSTAMP:20260404T094556Z
UID:TaoCollatz/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/TaoCo
 llatz/1/">The Collatz conjecture</a>\nby Terence Tao (UCLA) as part of The
  Collatz conjecture\n\n\nAbstract\nDefine the Collatz map Col on the natur
 al numbers by setting Col(n) to equal 3n+1 when n is odd and n/2 when n is
  even. The notorious Collatz conjecture asserts that all orbits of this ma
 p eventually attain the value 1. This remains open\, even if one is willin
 g to work with almost all orbits rather than all orbits. We show that almo
 st all orbits n\, Col(n)\, Col^2(n)\, ... eventually attain a value less t
 han f(n)\, for any function f that goes to infinity (no matter how slowly)
 . A key step is to obtain an approximately invariant (or more precisely\, 
 self-similar) measure for the (accelerated) Collatz dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/TaoCollatz/1/
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