Title: Fractals and Syzygies

Abstract: Syzygies are objects invented and utilized by David Hilbert in 1890 to study relations among polynomial equations, and have played a big role in the development of modern algebraic geometry. The quest to understand patterns of syzygies is both challenging and interesting, and sometimes reveals unexpected connections to other branches of mathematics. In this talk, I will describe recent joint work with David Eisenbud on monomials with linear syzygies.  It turns out that certain fractal structures that appear in many contexts, from game theory to number theory, play a significant role in building optimal examples.