Research

Preprints and Publications

• Educators Needed for a Quantum Future (with Justin Perron), Physics, 2022 (16) no. 59.

• Quantum money from quaternion algebras (with Daniel M. Kane and Alice Silverberg), Mathematical Cryptology, 2022 (2) no. 1, 60–83.

• Quantum Undergraduate Education and Scientific Training (with Justin K. Perron, Charles DeLeone, Tom Carter, Joshua M. Grossman, Gina Passante, and Joshua Sack), preprint 2021

• Geometry of biquadratic and cyclic cubic log-unit lattices (with Fernando Azpeitia Tellez and Christopher Powell), Journal of Number Theory, 2021 (228), 276–293.

• Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant (with Eric Rains, Karl Rubin, Travis Scholl, and Alice Silverberg), Algebra and Number Theory, 2021 (15) no. 3, 711–727.

• Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields (with Lisa Berger, Chris Hall, René Pannekoek, Jennifer Park, Rachel Pries, Alice Silverberg, and Douglas Ulmer), Memoirs of the American Mathematical Society 2020 (266), no. 1295
  

• Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves (with Dan Boneh, Darren Glass, Daniel Krashen, Kristin Lauter, Alice Silverberg, Mehdi Tibouchi, and Mark Zhandry), Journal of Mathematical Cryptology, 2020 (14), no. 1, 5–14.
  

• Period and index for higher genus curves, Journal of Number Theory, 2018 (186), 259–268
  

• A descent map for curves with totally degenerate semi-stable reduction, Journal de Théorie des Nombres de Bordeaux, 2013 (25) no. 1, 211–244.
  

• Period and index of genus one curves over number fields, Mathematische Annalen, 2012 (354) no. 3, 1029–1047.
  

• Period, index, and potential Sha (with Pete L. Clark), Algebra and Number Theory, 2010 (4) no. 2, 151–174.

• Curves with prescribed period and index over local fields, J. Algebra, 2007 (314) no. 1, 157–167.