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SUMMARY:Jonah Klein (University of South Carolina)
DTSTART:20260716T153000Z
DTEND:20260716T155500Z
DTSTAMP:20260710T111455Z
UID:CANT2026/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/48/
 ">The distortion method and its applications</a>\nby Jonah Klein (Universi
 ty of South Carolina) as part of Combinatorial and additive number theory 
 seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate
  Center (4th floor).\n\nAbstract\nA covering system is a finite set of ari
 thmetic progressions\, with the property that every integer belongs to at 
 least one of them. Covering systems were introduced by Erdös in 1950. In 
 the same article where he introduced them\, he asked if there was a unifor
 m upper bound on the smallest modulus of covering systems with distinct mo
 duli. This problem was resolved by Hough in 2015\, showing that the smalle
 st modulus is always smaller than $10^{16}$. Expanding upon his work\, Bal
 ister\, Bollobás\, Morris\, Sahasrabudhe\, and Tiba reduced this bound to
  $616 000$\, with a method that they coined the distortion method. The aim
  of this talk is to give a brief overview of the distortion method and its
  applications\, with a particular focus on showing that it is impossible t
 o construct 10 disjoint distinct covering systems. This is work in progres
 s with Michael Filaseta and Alexandros Kalogirou.\n
LOCATION:https://researchseminars.org/talk/CANT2026/48/
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