My primary research interests are in number theory and arithmetic geometry.  My thesis research used $(\phi, \Gamma)$-modules to study special values of $L$-functions and the equivariant Tamagawa number conjecture, which relates to both the Riemann zeta function and the Birch and Swinnerton-Dyer conjecture on elliptic curves.  You can find a copy of my thesis work here, and a preprint of my paper with Matthias Flach is here.