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SUMMARY:Pieter Allaart (University of North Texas)
DTSTART:20201110T133000Z
DTEND:20201110T143000Z
DTSTAMP:20260423T021437Z
UID:OWNS/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/23/">On
  the smallest base in which a number has a unique expansion</a>\nby Pieter
  Allaart (University of North Texas) as part of One World Numeration semin
 ar\n\n\nAbstract\nFor $x>0$\, let $U(x)$ denote the set of bases $q \\in (
 1\,2]$ such that $x$ has a unique expansion in base $q$ over the alphabet 
 $\\{0\,1\\}$\, and let $f(x)=\\inf U(x)$. I will explain that the function
  $f(x)$ has a very complicated structure: it is highly discontinuous and h
 as infinitely many infinite level sets. I will describe an algorithm for n
 umerically computing $f(x)$ that often gives the exact value in just a sma
 ll finite number of steps. The Komornik-Loreti constant\, which is $f(1)$\
 , will play a central role in this talk. This is joint work with Derong Ko
 ng\, and builds on previous work by Kong (Acta Math. Hungar. 150(1):194--2
 08\, 2016).\n
LOCATION:https://researchseminars.org/talk/OWNS/23/
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