Wednesday, March 14, 2007 - 11:15am - 12:15pm
The contents of this elementary talk grew out of my need to explain to non-mathematicians what I do for a living. I will pose (and solve) two old chessboard enumeration problems and a new problem. We will solve these by counting certain monomials, and this will naturally lead us to the notion of Hilbert functions. With these examples in mind, we will try and understand the simplest of monomial ideals, namely, edge ideals, and discover that these are not simple at all! On the way we will discover a new numerical invariant of forests.