My research is primarily in algebraic number theory and arithmetic geometry. I am currently interested in the arithmetic of algebraic curves.
- Odd degree isolated points on X1(N) with rational j-invariant (with A. Bourdon, D. Gill, and J. Rouse). (arxiv)
- On generalizations of the second Euclid-Mullin sequence (with J. Clark). (pdf)
Accepted and/or Published:
- ABC and the Hasse principle for quadratic twists of hyperelliptic curves (with P.L. Clark). C. R. Math. Acad. Sci. Paris 356 (2018), 911-915. (pdf)
- Varga’s theorem in number fields (with P.L. Clark). INTEGERS 18 (2018), A74, 11pp. (pdf)
- On isolated points of odd degree on X1(N), JMM NAM Haynes-Granville-Browne Session of Presentations by Recent Doctoral Recipients
- Hasse Principle Violations of Quadratic Twists of Hyperelliptic Curves,
JMM AMS Special Session on Arithmetic Statistics, January 18, 2019
- Hasse Principle Violations of Quadratic Twists of Hyperelliptic Curves, Connecticut Summer School in Number Theory (CTNT), University of Connecticut, June 1, 2018.
- 2-Selmer two ways, Graduate Student Seminar, The University of Georgia, November 28, 2017.
- An Introduction to P-orderings , Mock AMS Conference, The University of Georgia, July 29, 2015.