Mathematics Colloquium – Rick Miranda (Colorado State)

Interpolation for polynomials in two variables

Abstract: Suppose you want a polynomial f(x,y) to vanish at n specific points pi in the plane. If the points are not general, this is difficult; but what if you have general points? (We’ll mention what ‘general’ means in this setting.) If you only want the polynomial to vanish, this is elementary. Suppose you generalize to vanishing *with multiplicity*, i.e., the polynomial and all derivatives up to mi–1 must vanish (multiplicity mi). This is quite a bit more difficult, and is open for more than 9 points! I’ll discuss the various conjectures that have attracted attention, all of which are still open, and some recent progress. This is joint work with C. Ciliberto (Rome) and J. Roe’ (Barcelona).

Mathematics Colloquium Website