Title: Polynomial interpolation is harder than it sounds

Date: 09/22/2020

Time: 4:00 PM - 5:00 PM

Place: Online (virtual meeting)

Suppose that $(x_1,y_1),\ldots,(x_r,y_r)$ is a set of points in the plane. Given a degree $d$ and multiplicities $m_i$, does there a nonzero polynomial in two variables of degree at most $d$ which vanishes to order at least $m_i$ at $(x_i,y_i)$? What is the dimension of the space of such polynomials, and how does it vary with the parameters? I will explain some of the basic results and conjectures and show how this problem is connected to some questions of current interest in algebraic geometry.