Jack Huizenga, University of Illinois at Chicago
"Interpolation problems in algebraic geometry"
Classical
Lagrangian
interpolation
states
that
one
can
always
prescribe
$n+1$
values
of
a
single
variable
polynomial
of
degree
$n$.
This
result
paves
the
way
for
many
beautiful
generalizations
in
algebraic
geometry.
I
will
discuss
a
few
of
these
generalizations
and
their
relevance
to
important
questions
in
mathematics.
I
will
then
discuss
recent
connections
between
interpolation
problems
and
the
birational
geometry
of
Hilbert
schemes
of
points
and
moduli
spaces
of
vector
bundles.