On the Brumer--Stark conjecture

My research is in algebraic number theory, specifically the explicit construction of units in number fields and points on abelian varieties.  There are many classical conjectures regarding the relationships between these elements and special values of L-functions, such as the conjectures of Stark, Birch-Swinnerton-Dyer, and Beilinson.  In my research I have made progress on these conjectures as well as stated and studied various generalizations and refinements that go beyond the world of L-functions.  Much of my work uses the theory of modular forms and their associated Galois representations in order to shed light on these problems.