
Ph.D., Princeton University (2006)
Research Interests
My mathematical interests lie in algebraic number theory and arithmetic algebraic geometry.

Papers
Local points of supersingular elliptic curves on Zpextensions, in preparation.
Localglobal trace questions and twists of genus one curves (with E. Ozman), preprint.
padic heights of Heegner points and adic regulators (with J. Balakrishnan and W. Stein), submitted.
Weil–Chatelet divisible elements in Tate–Shafarevich groups II: On a question of Cassels (with J. Stix), "to appear in Journal fur die Reine und Angewandte Mathematik. "
Galois sections for abelian varieties over number ﬁelds (with J. Stix), submitted.
Weil–Chatelet divisible elements in Tate–Shafarevich groups I: Bashmakov’s problem for elliptic ˆcurves over Q (with J. Stix), to appear in Compositio Mathematica.
Relative Brauer groups of genus 1 curves (with D. Krashen), Israel Journal of Mathematics 192 (2012), 921–949.
TateShafarevich groups in anticyclotomic Zpextensions at supersingular primes, Compositio Mathematica 145 (2009), 293–308.
Solvable points on genus one curves (with A. Wiles), Duke Mathematical Journal 142 (2008), no. 3, 381–464.

 Spring 2011 College of Natural Sciences Teaching Excellence Award.
 2000 Member of the Phi Beta Kappa Society, the Sigma Xi Society, the AMS and AWM.