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SUMMARY:Jakub Konieczny (Claude Bernard University Lyon 1\, France)
DTSTART:20220525T143000Z
DTEND:20220525T145500Z
DTSTAMP:20260423T011438Z
UID:CANT2022/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/19/
 ">Automatic semigroups</a>\nby Jakub Konieczny (Claude Bernard University 
 Lyon 1\, France) as part of Combinatorial and additive number theory (CANT
  2022)\n\n\nAbstract\nAutomatic sequences\, that is\, sequences computable
  by finite automata\, have been extensively studied from a variety of pers
 pectives\, including combinatorics\, number theory\, dynamics and theoreti
 cal computer science. Classification problems are a natural class of quest
 ions in the theory of automatic sequences. In particular\, the problem of 
 classifying automatic multiplicative sequences has attracted considerable 
 attention\, culminating in complete classification which we obtained in jo
 int work with Clemens M\\"{u}llner and Mariusz Lema\\'{n}czyk. The subject
  of my talk will be an extension of this line of inquiry\, which we pursue
  in joint work with Oleksiy Klurman. Under mild technical assumptions\, we
  classify all automatic multiplicative semigroups\, that is\, all sets $E$
  of integers which are closed under multiplication and such that the indic
 ator function $1_E$ is automatic. Additionally\, we show (again\, under mi
 ld technical assumptions) that if $E\,F$ are automatic sets with $E \\cdot
  F \\subset E$ then $E$   must contain a large essentially periodic compon
 ent. This leads to potentially interesting open problems concerning produc
 ts of automatic sets.\n
LOCATION:https://researchseminars.org/talk/CANT2022/19/
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