Professor Weston studies the interplay between L-functions and certain arithmetic objects known as Selmer groups. Selmer groups are generalizations of ideal class groups and the group of rational points on an elliptic curve which distill the information contained in p-adic representations of the absolute Galois group. He has used such relations to enlarge dramatically the number of cases in which one can precisely compute universal deformation rings as in the work of Wiles. Jointly with Robert Pollack of Boston University, he also studies the behavior of L-functions and Selmer groups of modular forms in certain p-adic analytic families. In many cases they are able to show that one can use values of the L-functions (which are relatively computable) to compute Selmer groups (which are a priori very difficult to compute).