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SUMMARY:Laurence P. Wijaya (University of Kentucky)
DTSTART:20260718T193000Z
DTEND:20260718T195500Z
DTSTAMP:20260805T044341Z
UID:CANT2026/90
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/90/
 ">Polynomial corners over finite field</a>\nby Laurence P. Wijaya (Univers
 ity of Kentucky) as part of Combinatorial and additive number theory semin
 ar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate Cent
 er (4th floor).\n\nAbstract\nRecently there has been some progress in unde
 rstanding the density of a subset of $[N]^2$ that avoids polynomial patter
 ns. Kravitz\, Kuca\, and Leng showed that if $P\\in\\Z[z]$ satisfies certa
 in conditions\, then any set $A\\subseteq[N]^2$ does not contain $(x\,y)\,
 (x+P(z)\,y)\,(x\,y+P(z))$\, we must have \n \\[\n |A|\\ll_P\\frac{N^2}{(\\
 log\\log\\log N)^c}\n \\]\n for some small constant $c$. \n \n In this tal
 k\, we show a similar result in $(\\F_p)^2$ where we get a better bound on
  the density of a set $A\\subseteq (\\F_p)^2$ not containing $(x\,y)\,(x+P
 (z)\,y)\,(x\,y+P(z))$ with some conditions on $P\\in \\F_p[z]$.\n
LOCATION:https://researchseminars.org/talk/CANT2026/90/
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