Here is my CV.
Currently, I am looking problems in arithmetic statistics. With Daniel Keliher, I am studying the difference between and quartic extensions of number fields. Over the rational numbers, we know that 83% of quartic extensions have a Galois closure with Galois group and the other 17% have Galois group . If you look at quartic extensions of an arbitrary number field instead of , this changes.
Before graduate school, I worked on some problems in computational number theory studying the discrete log problem. This started with an REU at Rose-Hulman in 2010 and continued in the years before I started at Tufts. We modeled the function as graph and collected data for a range of prime numbers to see if these graphs looked “random.”
- Friedrichsen, M., Larson, B., McDowell, E. Structure and Statistics of the Self-Power Map. Rose-Hulman Undergraduate Math Journal, Vol 11, Issue 2, Article 6.
- Friedrichsen, M., Holden, J. Statistics for fixed points of the self-power map. Involve, Vol 12, Issue 1.