Suppose that (x_1,y_1),...,(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.


Zoom information: https://umich.zoom.us/j/97646405029

passcode: 993219 Speaker(s): John Lesieutre (Penn State University)