Limits of moduli spaces in the Grothendieck ring
-- Melanie Matchett Wood, November 10, 2017

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We will see there is a well defined limit, in the
Grothendieck ring of varieties, of several different sequences of
moduli spaces. In flavor, these are algebro-geometric analogs of topological results about homological
stability, or of arithmetic results about asymptotics of points counts
on moduli spaces.  For example, we determine the limit of the motive
of smooth divisors (or with s singularities) in increasing multiples
of a linear system. We also determine the limit of the motive of
configuration spaces of distinct points (or points that are allowed to
come together to a limited extent) as the number of points increases.
All of these limits in the Grothendieck ring are given by explicit
formulas in terms of motivic zeta values. Our results motivate a large
number of conjectures in topology and arithmetic.  This is joint work
with Ravi Vakil.