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SUMMARY:Jared Duker Lichtman (Stanford University)
DTSTART:20260713T190000Z
DTEND:20260713T195000Z
DTSTAMP:20260710T111702Z
UID:CANT2026/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/18/
 ">Primitive sets and von Mangoldt chains: Erdős #1196 and beyond</a>\nby 
 Jared Duker Lichtman (Stanford University) as part of Combinatorial and ad
 ditive number theory seminar (CANT 2026)\n\nLecture held in Science Center
  in the CUNY Graduate Center (4th floor).\n\nAbstract\nA set of integers i
 s primitive if no number in the set divides another. We introduce a new me
 thod for bounding Erdős sums of primitive sets\, suggested from output of
  GPT-5.4 Pro\, based on Markov chains with von Mangoldt weights. The metho
 d leads to a host of applications\, yet seems to have been overlooked by t
 he prior literature since Erdős' seminal 1935 paper. As applications\, we
  prove two 1966 conjectures of Erdős-Sárközy-Szemerédi\, on primitive 
 sets of large numbers (#1196) and on divisibility chains (#1217). The meth
 od also provides a short proof of the Erdős Primitive Set Conjecture (#16
 4)\, as well as the related claim that 2 is an ``Erdős-strong'' prime. Mo
 reover\, the method resolves a revised form of the Banks-Martin conjecture
 \, which has long been viewed as a unifying ``master theorem'' for the are
 a. Joint work with B. Alexeev\, K. Barreto\, Y. Li\, L. Price\, J. I. Shah
 \, Q. Tang\, and T. Tao.\n
LOCATION:https://researchseminars.org/talk/CANT2026/18/
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