Equidistribution of Shapes of Number Fields of degree 3, 4, and 5

In her talk, Piper Harron will introduce the ideas that there are number fields, that number fields have shapes, and that these shapes are everywhere you want them to be.  This result is joint work with Manjul Bhargava and uses his counting methods which currently we only have for cubic, quartic, and quintic fields.  She will sketch the proof of this result and leave the rest as an exercise for the audience.  (Check your work by downloading her thesis!)