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SUMMARY:Shabnam Akhtari (University of Oregon)
DTSTART:20200625T173000Z
DTEND:20200625T183000Z
DTSTAMP:20260423T004136Z
UID:MAGIC/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAGIC/8/">A 
 positive proportion of quartic binary forms does not represent 1.</a>\nby 
 Shabnam Akhtari (University of Oregon) as part of MAGIC (Michigan - Arithm
 etic Geometry Initiative - Columbia)\n\n\nAbstract\nI will discuss an expl
 icit construction of many equations of the shape F(x \, y) = 1 which have 
 no solutions in integers x\, y\, where F(x \, y) is a quartic form with in
 teger coefficients. In this recent work\, in order to construct a dense su
 bset of forms that do not represent 1\,  the quartic forms are ordered by 
 the two generators of their rings of invariants. In a previous  joint work
  with Manjul Bhargava\, we showed a similar result\, but we ordered forms 
 by their naive heights.\n
LOCATION:https://researchseminars.org/talk/MAGIC/8/
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