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SUMMARY:Nathan Kaplan (University of California\, Irvine)
DTSTART:20240328T170000Z
DTEND:20240328T180000Z
DTSTAMP:20260423T024754Z
UID:UAANTS/87
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/87/">
 Codes from varieties over finite fields</a>\nby Nathan Kaplan (University 
 of California\, Irvine) as part of University of Arizona Algebra and Numbe
 r Theory Seminar\n\nLecture held in ENR2 N595.\n\nAbstract\nThere are $q^{
 20}$ homogeneous cubic polynomials in four variables with coefficients in 
 the finite field $F_q$. How many of them define a cubic surface with $q^2+
 7q+1$ $F_q$-rational points? What about other numbers of rational points? 
 How many of the $q^{20}$ pairs of homogeneous cubic polynomials in three v
 ariables define cubic curves that intersect in 9 $F_q$-rational points? Th
 e goal of this talk is to explain how ideas from the theory of error-corre
 cting codes can be used to study families of varieties over a fixed finite
  field. We will not assume any previous familiarity with coding theory. We
  will start from the basics and emphasize examples.\n
LOCATION:https://researchseminars.org/talk/UAANTS/87/
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