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SUMMARY:Renling Jin (College of Charleston)
DTSTART:20220526T153000Z
DTEND:20220526T155500Z
DTSTAMP:20260423T011341Z
UID:CANT2022/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/36/
 ">Hyper-hyper-hyper-integers</a>\nby Renling Jin (College of Charleston) a
 s part of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstra
 ct\nIn a conference five years ago\, T. Tao reported \nhis effort to simpl
 ify Szemer\\'{e}di's original combinatorial proof of \nSzemer\\'{e}di's th
 eorem using nonstandard analysis. \nWe continued his effort and presented 
 a simple proof of\nthe theorem for $k=4$ in CANT 2020. In this talk\, we w
 ill present \na simple proof of the theorem for all $k$. One of the main s
 implifications\nis that a Tower of Hanoi type induction used by Szemer\\'{
 e}di as well as Tao\nis replaced by a straightforward induction. In the pr
 oof the integers with\nthree levels of infinities are used.\n
LOCATION:https://researchseminars.org/talk/CANT2022/36/
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