Pure Mathematics special colloquium

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.