Silas Johnson
I research arithmetic statistics, which is a branch of number theory concerned with questions like the following:

How many number fields (in a given family) are there of discriminant less than X? How does this behave as X goes to infinity?

In general, this is very hard, and the answer is known only for a few families of number fields. I am interested in investigating some related questions:

  • Can we replace the discriminant (in the original question) by something else?
  • What are reasonable things to replace it with?
  • How should we expect the answer to change when we use one of these "alternate discriminants"?

Thinking about these questions requires input from the Malle-Bhargava heuristics for number field counting, a lot of Galois theory of local and global fields, and a deep understanding of what the discriminant is and how to interpret it.

Preprint: S. Johnson, Weighted Discriminants and Mass Formulas for Number Fields (submitted).

Department of Mathematics, Northwestern University
2033 Sheridan Road; Evanston, IL 60208
Email: sjohnson at math dot northwestern dot edu
Office: Locy 202