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SUMMARY:Dmytro Karvatskyi (Institute of Mathematics\, Natl. Acad. Sci. Ukr
 aine\; University of St. Andrews)
DTSTART:20250424T123000Z
DTEND:20250424T140000Z
DTSTAMP:20260423T004912Z
UID:fran/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/67/">Ca
 ntorvals: emergence\, structure\, open problems</a>\nby Dmytro Karvatskyi 
 (Institute of Mathematics\, Natl. Acad. Sci. Ukraine\; University of St. A
 ndrews) as part of Семінар з фрактального аналіз
 у / Fractal analysis seminar\n\n\nAbstract\nThis talk is dedicated to the
  study of Cantorvals—perfect sets on the real line with nonempty interio
 r and fractal boundaries. Such sets emerge naturally in various areas of m
 athematics\, 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 poorly unde
 rstood due to their intricate internal structure. In this talk\, we establ
 ish conditions under which the set of incomplete sums of a generalized mul
 tigeometric series forms a Cantorval. We also examine the structure of suc
 h Cantorvals within a certain one-parameter family. Finally\, several open
  problems related to the topic will be discussed.\n\nThis is joint work wi
 th Professors Mykola Pratsiovytyi\, Aniceto Murillo\, and Antonio Viruel.\
 n
LOCATION:https://researchseminars.org/talk/fran/67/
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