My name is Matt Friedrichsen. I am a third year PhD student in mathematics at Tufts University. My advisor is Robert Lemke Oliver, and my main research interest is number theory. I graduated with a Bachelor’s degree from St. Olaf College in 2011, and my Master’s from Tufts in 2019.

CV

Here is my CV.

Research

Currently, I am looking problems in arithmetic statistics. With Daniel Keliher, I am studying the difference between S_4 and D_4 quartic extensions of number fields. Over the rational numbers, we know that 83% of quartic extensions have a Galois closure with Galois group S_4 and the other 17% have Galois group D_4. If you look at quartic extensions of an arbitrary number field instead of \mathbb{Q}, 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 f(x) = x^x \pmod{p} as graph and collected data for a range of prime numbers to see if these graphs looked “random.”

Publications

  • 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.