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SUMMARY:Dmytro Karvatskyi (Institute of Mathematics\, Natl. Acad. Sci. Ukr
 aine\; University of St. Andrews)
DTSTART:20250501T123000Z
DTEND:20250501T140000Z
DTSTAMP:20260423T004800Z
UID:fran/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/68/">Ca
 ntorvals: emergence\, structure\, open problems (part 2)</a>\nby Dmytro Ka
 rvatskyi (Institute of Mathematics\, Natl. Acad. Sci. Ukraine\; University
  of St. Andrews) as part of Семінар з фрактального а
 налізу / Fractal analysis seminar\n\n\nAbstract\nThis talk is dedica
 ted to the study of Cantorvals—perfect sets on the real line with nonemp
 ty interior and fractal boundaries. Such sets emerge naturally in various 
 areas of mathematics\, including the study of sets of subsums of numerical
  series\, arithmetic sums of Cantor-like sets\, and attractors of iterated
  function systems. Despite their frequent appearance\, Cantorvals remain p
 oorly understood due to their intricate internal structure. In this talk\,
  we establish conditions under which the set of incomplete sums of a gener
 alized multigeometric series forms a Cantorval. We also examine the struct
 ure of such Cantorvals within a certain one-parameter family. Finally\, se
 veral open problems related to the topic will be discussed.\n\nThis is joi
 nt work with Professors Mykola Pratsiovytyi\, Aniceto Murillo\, and Antoni
 o Viruel.\n
LOCATION:https://researchseminars.org/talk/fran/68/
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