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SUMMARY:Laurent Bienvenu (Université de Bordeaux)
DTSTART:20201110T140000Z
DTEND:20201110T150000Z
DTSTAMP:20260423T005715Z
UID:CTA/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/35/">The
  interplay between randomness and genericity</a>\nby Laurent Bienvenu (Uni
 versité de Bordeaux) as part of Computability theory and applications\n\n
 \nAbstract\nIn computability theory\, one often think of (Cohen)-genericit
 y and algorithmic randomness as orthogonal notions: a truly random real wi
 ll look very non-generic\, and a truly generic real will look very non-ran
 dom. This orthogonality is best incarnated by the result of Nies\, Stephan
  and Terwijn that any 2-random real and 2-generic real form a minimal pair
  for Turing reducibility. On the other hand\, we know from the Kucera-Gacs
  theorem that for any n there is a 1-random real which computes an n-gener
 ic one\, but also (and more surprisingly)\, by a result of Kautz that ever
 y 2-random real computes a 1-generic real. These last two results tell us 
 that the interplay between randomness and genericity is rather complex whe
 n “randomness” is between 1-random and 2-random or “genericity” be
 tween 1-generic and 2-generic. It is this gray area that we will discuss i
 n this talk (based on the paper of the same title\, joint work with Chris 
 Porter).\n
LOCATION:https://researchseminars.org/talk/CTA/35/
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