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SUMMARY:Veronica Bitonti (University of Oxford\, UK)
DTSTART:20260717T173000Z
DTEND:20260717T175500Z
DTSTAMP:20260710T111503Z
UID:CANT2026/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/68/
 ">Gap sets of random generalized numerical semigroups</a>\nby Veronica Bit
 onti (University of Oxford\, UK) as part of Combinatorial and additive num
 ber theory seminar (CANT 2026)\n\nLecture held in Science Center in the CU
 NY Graduate Center (4th floor).\n\nAbstract\nFor a fixed positive integer 
 $d$ and a small real $p>0$\, sample a $p$-random subset $A \\subseteq \\ma
 thbb{Z}_{\\geq 0}^d$\, and let $S:=\\langle A \\rangle$ be the generalized
  numerical semigroup generated by $A$. We show that\, with high probabilit
 y (as $p \\to 0$)\, the gap set $\\mathbb{Z}_{\\geq 0}^d \\setminus S$ is 
 well approximated by the shifted hyperboloid region $$\\{(x_1\, \\ldots\, 
 x_d) \\in \\mathbb{R}_{\\geq 0}^d: (x_1+\\log p^{-1}) \\cdots (x_d+\\log p
 ^{-1})\\ll p^{-1}(\\log p^{-1})^{d+1}\\}.$$ This generalizes work of Kravi
 tz\, Morales\, and Schildkraut on the $1$-dimensional setting. We also obt
 ain the same result with $S$ replaced by the set of subset sums of $A$. Th
 is is a joint work with Noah Kravitz.\n
LOCATION:https://researchseminars.org/talk/CANT2026/68/
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