Research

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.