Back to Departmental Colloquium: Spring 2014
Departmental Colloquium
Date: Thursday, Feb 13, 2014
Time: 4:00PM
Location: LCB 219
Karl Schwede
Pennsylvania State University
Title |
Singularities of polynomials -- multiplier ideals, test ideals and alterations |
Abstract |
We will consider solution sets to polynomial equations. For example, consider y^2 = x^3, the solution set has a singularity at the origin (a cusp). I will talk about different ways to measure singularities such as this one. First I will discuss the multiplier ideal, a way to measure singularities via integration. Second I will discuss the test ideal, a way to measure singularities if one considers them over a finite field. It has been known for nearly two decades that these two independently introduced notions are closely related. I will discuss recent joint work with Manuel Blickle and Kevin Tucker which shows that these two objects are in fact aspects of the same phenomenon. |
Commutative Algebra