Research

Selected Publications

• “Picard curves over $\mathbb{Q}$ with good reduction away from $3$,” with Beth Malmskog (submitted). arXiv: 1407.7892. [arXiv]
• “Arithmetic of abelian varieties with constrained torsion,” with Akio Tamagawa, to appear in Transactions of the American Mathematical Society. arXiv:1302.1477. [arXiv]
• “Character sums determined by low degree isogenies of elliptic curves,” with Dustin Moody, to appear in Rocky Mountain Journal of Mathematics. arXiv:1210.2743. [arXiv]
• “Class number formulas via $2$-isogenies of elliptic curves,” with Cam McLeman, Bulletin of the London Mathematical Society, 44 (2012), 1221-1236. [Journal] [arXiv]
• “An abelian surface with constrained $3$-power torsion,” in Advanced Studies in Pure Mathematics 63: Galois-Teichmüller Theory and Arithmetic Geometry, Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa eds., Mathematical Society of Japan, 449-456. [pdf]
• “On elliptic curves of conductor $11^2$ and an open question of Ihara,” Algebraic number theory and related topics 2007, 101-113, RIMS Kôkyûroku Bessatsu, B12, Res. Inst. Math. Sci. (RIMS), Kyoto, 2009. [Journal]
• “A finiteness conjecture on abelian varieties with constrained prime power torsion,” Mathematical Research Letters vol. 15, issue 6, 1223-1231. [Journal]
• “On the torsion of Jacobians of principal modular curves of level $3^n$,” Archiv der Mathematik vol. 88, issue 1, 19-28, 2007. [Journal] [arXiv]
• “On the fields of $2$-power torsion of certain elliptic curves,” Mathematical Research Letters 11, 529-538, 2004. [Journal]