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SUMMARY:Margaret Bilu (NYU)
DTSTART:20200612T174500Z
DTEND:20200612T184500Z
DTSTAMP:20260407T214640Z
UID:agstanford/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/1
 4/">Arithmetic and motivic statistics via zeta functions</a>\nby Margaret 
 Bilu (NYU) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nT
 he Grothendieck group of varieties over a field $k$ is the quotient of the
  free abelian group on isomorphism classes of algebraic varieties over k b
 y the so-called cut-and-paste relations. Many results in number theory hav
 e a natural motivic analogue which can be formulated in the Grothendieck r
 ing of varieties. For example\, Poonen's finite field Bertini theorem has 
 a motivic counterpart due to Vakil and Wood\, though none of the two state
 ments can be deduced from the other. We describe a conjectural way to unif
 y the number-theoretic and motivic statements (when the base field is fini
 te) in this and other examples\, and will provide some evidence towards it
 . A key step is to reformulate everything in terms of convergence of zeta 
 functions of varieties in several different topologies. This is joint work
  with Ronno Das and Sean Howe.\n
LOCATION:https://researchseminars.org/talk/agstanford/14/
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