The integral closure of an ideal I is an ideal lying between I itself and the radical of I. It is an important object in commutative algebra, but one which is not well understood. I will begin by presenting a conjecture about the integral closure of ideals generated by the partial derivatives of a polynomial f, and discussing its connection to Wiles' proof of Fermat's Last Theorem. The rest of the talk will focus on the case of monomial ideals, which is much easier to understand. Here the integral closure of I has a nice description as a convex hull of points, so we can calculate it just by drawing pictures. If there is time, I will show how this convex hull also gives us another object, the adjoint of I, and say why this is important for what my research.
To volunteer to give a talk, or for any other questions regarding this schedule, contact Sara Miller