My research is primarily in algebraic number theory and arithmetic geometry. I am currently interested in the arithmetic of algebraic curves.

Research Papers

   Preprints:

• Hasse principle violations in twist families of superelliptic curves. (pdf)
• 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)

Upcoming Talks

•  (TBD) Appalachian State University. April 30, 2021.

Previous Talks

• On isolated points of odd degree on X1(N). 
  JMM NAM Haynes-Granville-Browne Session of Presentations by Recent Doctoral Recipients. January 7, 2021.
• Odd degree isolated points on X1(N) with rational j-invariant.
  University of Washington. December 1, 2020.
• Hasse Principle Violations of Quadratic Twists of Hyperelliptic Curves. 
  Center for Computing Sciences Seminar. February 2020
• 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.