BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mark Shusterman (Harvard)
DTSTART:20200723T173000Z
DTEND:20200723T183000Z
DTSTAMP:20260423T024507Z
UID:MAGIC/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAGIC/12/">T
 he quadratic Bateman-Horn conjecture over function fields</a>\nby Mark Shu
 sterman (Harvard) as part of MAGIC (Michigan - Arithmetic Geometry Initiat
 ive - Columbia)\n\n\nAbstract\nAre there infinitely many natural numbers $
 n$ with $n^2+1$ a prime?\n\nIn a joint work in progress with Will Sawin we
  show that for some finite fields $F$\, there are infinitely many monic po
 lynomials $f \\in F[u]$ for which $f^2 + u$ is prime (i.e. monic irreducib
 le).\n\nAfter surveying some earlier works\, I’ll explain how to reduce 
 the problem to a question of cancellation in an incomplete exponential sum
 . Via the Grothendieck-Lefschetz trace formula\, this will lead us to boun
 ding the cohomology of certain sheaves on the complement of a hyperplane a
 rrangement in affine space.\n
LOCATION:https://researchseminars.org/talk/MAGIC/12/
END:VEVENT
END:VCALENDAR