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SUMMARY:Noah Kravitz (Oxford University\, UK)
DTSTART:20260716T133000Z
DTEND:20260716T135500Z
DTSTAMP:20260710T111543Z
UID:CANT2026/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/44/
 ">Sets with few subset sums</a>\nby Noah Kravitz (Oxford University\, UK) 
 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 classical result of Nathanson shows that every $n$-element s
 et of positive reals has at least $\\binom{n+1}{2}+1$ distinct subset sums
 \, with equality exactly for homogeneous arithmetic progressions. We estab
 lish stability versions of this inverse theorem in two regimes. First\, fo
 r any parameter $0 \\leq M \\leq n-4$\, we precisely characterize the $n$-
 element sets of positive reals with at most $\\binom{n+1}{2}+1+M$ subset s
 ums. Second\, for any constant $C$\, we provide a characterization\, sharp
  up to constants\, of the $n$-element sets of positive reals with at most 
 $Cn^2$ distinct subset sums. Joint work with Ruben Carpenter and Colin Def
 ant.\n
LOCATION:https://researchseminars.org/talk/CANT2026/44/
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