The talk describes joint work with Tigran Ananyan. By a theorem of F.S. Macaulay, for any homogeneous ideal in a polynomial ring over a field there is a unique lex ideal (a monomial ideal such that the if m' > m are monomials of the same degree and m is in the lex ideal, then so is m') with the same Hilbert function. Suppose one fixes a homogeneous ideal involving h variables and then considers the extended ideal to the polynomial ring in N variables for N >> 0. It turns out that the least number of generators of the corresponding lex ideal often grows with N. In fact, for quadratic regular sequences of length two, the least numbers of generators have double exponential growth and are almost the same as a sequence of numbers introduced by Hamilton in a completely different context. Speaker(s): Mel Hochster (University of Michigan)