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SUMMARY:Ratko Darda (Sabancı)
DTSTART:20250509T124000Z
DTEND:20250509T134000Z
DTSTAMP:20260423T052645Z
UID:OBAGS/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/68/">M
 anin's Conjecture and stacks</a>\nby Ratko Darda (Sabancı) as part of ODT
 U-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nGiven a system of pol
 ynomial equations\, one may ask how many solutions it has in the rational 
 numbers. If there are infinitely many\, we further ask about the number of
  solutions of bounded "size." The answer depends heavily on the geometry o
 f the variety defined by the system. When the variety is Fano—meaning th
 at the top wedge power of the tangent bundle is ample—the "correct" math
 ematical framework is provided by Manin's conjecture\, which predicts the 
 asymptotic number of rational points of bounded height.\n\nAnother importa
 nt conjecture in a similar spirit is Malle's conjecture\, which predicts t
 he number of Galois extensions of the rational numbers with bounded discri
 minant.\n\nWe explain how both conjectures can be viewed as special cases 
 of a single conjecture concerning the number of rational points of bounded
  height on stacks. We then discuss some recent advances\, including the po
 sitive characteristic. This talk is based on joint work with Takehiko Yasu
 da.\n
LOCATION:https://researchseminars.org/talk/OBAGS/68/
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