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SUMMARY:Ronnie Pavlov (University of Denver)
DTSTART:20230425T130000Z
DTEND:20230425T140000Z
DTSTAMP:20260423T021339Z
UID:OWNS/114
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/114/">S
 ubshifts of very low complexity</a>\nby Ronnie Pavlov (University of Denve
 r) as part of One World Numeration seminar\n\n\nAbstract\nThe word complex
 ity function $p(n)$ of a subshift $X$ measures the number of $n$-letter wo
 rds appearing in sequences in $X$\, and $X$ is said to have linear complex
 ity if $p(n)/n$ is bounded. It's been known since work of Ferenczi that su
 bshifts X with linear word complexity function (i.e. $\\limsup p(n)/n$ fin
 ite) have highly constrained/structured behavior. I'll discuss recent work
  with Darren Creutz\, where we show that if $\\limsup p(n)/n < 4/3$\, then
  the subshift $X$ must in fact have measurably discrete spectrum\, i.e. it
  is isomorphic to a compact abelian group rotation. Our proof uses a subst
 itutive/S-adic decomposition for such shifts\, and I'll touch on connectio
 ns to the so-called S-adic Pisot conjecture.\n
LOCATION:https://researchseminars.org/talk/OWNS/114/
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