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SUMMARY:Terence Tao (UCLA)
DTSTART:20200414T220000Z
DTEND:20200414T230000Z
DTSTAMP:20260422T212834Z
UID:TaoCollatz/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TaoCollatz/1
 /">The Collatz conjecture</a>\nby Terence Tao (UCLA) as part of The Collat
 z conjecture\n\n\nAbstract\nDefine the Collatz map Col on the natural numb
 ers 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 map event
 ually attain the value 1. This remains open\, even if one is willing to wo
 rk with almost all orbits rather than all orbits. We show that almost all 
 orbits n\, Col(n)\, Col^2(n)\, ... eventually attain a value less than 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-si
 milar) measure for the (accelerated) Collatz dynamics.\n
LOCATION:https://researchseminars.org/talk/TaoCollatz/1/
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