Papers
The Square Threshold Problem in Number Fields (PDF)
Master's Thesis | Clemson University
Given an arbitrary number field and the corresponding ring of integers, we determine a probabilistic bound on the number of ideals of a specified norm that would need to be randomly selected with uniform probability before the product of some subset of these ideals is a square.
Notes
- Hida Theory (PDF) - My comprehensive exam paper on the basics of Hida theory, focusing on the material found in chapter 7 of Hida's Elementary theory of L-functions and Eisenstein series.
Talks
- "Math is Everywhere" (PowerPoint) - This the PowerPoint presentation I gave to St. Michael's Parish Day School students and their parents for their Family Math Night. The presentation explores a few of the many unexpected ways mathematics shows up in nature.