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SUMMARY:Kevin O'Bryant (CUNY)
DTSTART:20260713T130000Z
DTEND:20260713T132500Z
DTSTAMP:20260710T111504Z
UID:CANT2026/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/1/"
 >The Sidon error term</a>\nby Kevin O'Bryant (CUNY) as part of Combinatori
 al and additive number theory seminar (CANT 2026)\n\nLecture held in Scien
 ce Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA Sidon se
 t is a set ${\\mathcal A}$ of integers that has no nontrivial solutions to
  $a+b=c+d$. It has been known since 1941 (Erd\\H{o}s and Tur\\'an) that if
  ${\\mathcal A}$ is a finite Sidon set\, then $\\text{diam}({\\mathcal A})
  \\ge k^2 - 2k^{3/2} + O(k)$\, and since 1939 (Singer) that the $k^2$ term
  cannot be improved. Only in the last 5 years has the error term $-2k^{3/2
 }$ been sharpened (Balogh\, F\\"uredi\, and Roy\, then O'Bryant\, then Car
 ter\, Hunter\, O'Bryant). In this talk\, I will relay the latest improveme
 nts and applications\, and the use of AI (AlphaEvolve) in their discovery.
  Joint work with D.~Carter\, B.~Georgiev\,  Z.~Hunter\, J.~G.~Serrano\, T.
 ~Tao\, and A.~Zs.~Wagner.\n
LOCATION:https://researchseminars.org/talk/CANT2026/1/
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