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SUMMARY:Peter Koymans (Max Planck Institute)
DTSTART:20200618T173000Z
DTEND:20200618T183000Z
DTSTAMP:20260423T004140Z
UID:MAGIC/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAGIC/4/">In
 tegral points on quadratic equations</a>\nby Peter Koymans (Max Planck Ins
 titute) as part of MAGIC (Michigan - Arithmetic Geometry Initiative - Colu
 mbia)\n\n\nAbstract\nFix a prime number $l \\equiv 3 \\bmod 4$. In this ta
 lk we study how often the equation $x^2 - dy^2 = l$ is soluble in integers
  x and y as we vary $d$ over squarefree integers divisible by our fixed pr
 ime $l$. We will discuss how this question can be rephrased in terms of th
 e 2-part of the narrow class group of $\\mathbb{Q}(\\sqrt{d})$. Then we sk
 etch how one can use the recent ideas of Alexander Smith to obtain the dis
 tribution of these class groups. This is joint work with Carlo Pagano.\n
LOCATION:https://researchseminars.org/talk/MAGIC/4/
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