Publications


  1. Chabauty-Coleman experiments for genus 3 hyperelliptic curves, submitted. (Joint with J. Balakrishnan, F. Bianchi, V. Cantoral-Farfan, and M. Ciperiani) pdf
  2. A local-global principle for images of Galois representations, submitted. pdf
  3. On the ranks of the Jacobians of curves defined by Jacobi polynomials. Rocky Mountain J. Math., 44 no. 1 (2014), pp. 23 - 33. (Joint with J. Cullinan and E. Sell) pdf
  4. Powers of the eta-function and Hecke operators. Int. J. Number Theory, 8 no. 3 (2012), pp. 599 - 611. (Joint with A. Carney and S. Pitman) pdf
  5. Evaluations of cubic twisted Kloosterman sheaf sums. Int. J. Number Theory, 6 no. 6 (2010), pp. 1349-1365. (Joint with J. Booher and A. Hittson) pdf


In Preparation


  1. A classification of algebraic function fields with class number 3.
  2. Sporadic cubic torsion. (Joint with M. Derickx, M. van Hoeij, J. Morrow, and D. Zureick-Brown)
  3. Explicit Brauer-Manin obstructions for 9-nodal cubic threefolds (Joint with M. Pieropan and B. Frankel)


Slides


Warning: Some of these may be out of date as the papers were not written at the time.

  1. "Chabauty-Coleman experiments for genus 3 hyperelliptic curves," Rational and Integral points via Analytic and Geometric Methods in Oaxaca, Mexico. pdf
  2. "Sporadic Torsion on Elliptic Curves," AMS Sectional Meetings: Special Session on Numbers, Functions, Transcendence, and Geometry in Denton, TX. pdf
  3. "Sporadic Torsion on Elliptic Curves," Rice Colloquium in Houston, TX. pdf
  4. "Class numbers of algebraic function fields, or Jacobians of curves over finite fields," AMS Special Session on Number Theory and Cryptography at the 2016 Joint Mathematics Meetings in Seattle, WA. pdf