My research has produced new methods for studying prime splitting in global field extensions. I have also investigated potential generalizations of the Neukirch-Uchida Theorem via the arithmetic of corresponding abelian extensions of number fields. I’m currently thinking about splitting statistics and looking into geometric L-functions as moduli with Ben McReynolds. If you’re interested, click to see my full CV and Research Statement.
- Corresponding Abelian Extensions of Integrally Equivalent Number Fields, J. Number Theory, arXiv.
- Exceptional Primes in Notions of Arithmetic Similarity, submitted, arXiv.
- Strong Multiplicity One for Goss Zeta and its Teichmüller Lift, submitted, arXiv.
- Spectral and Geometric L-functions as Moduli, in progress (joint with Ben McReynolds).
- The Geometric L-function Group as a Topological Invariant, in progress (joint with Ben McReynolds).
- Exceptional Primes in Notions of Arithmetic Similarity II, in progress.