Stickelberger elements of non-ordinary modular forms

In this talk, we will discuss progress on attaching analytic Iwasawa invariants to modular forms with non-ordinary reduction at some prime p. These invariants should neatly encode the p-adic valuations of special values of the corresponding complex L-series. For forms of weight 2, such invariants were first defined by Perrin-Riou, and in a previous talk (in this seminar!) we discussed the case of weight p+1. We now aim to give a more general picture -- interestingly, the structure of the residual representation of f restricted to a decomposition group at p plays a pivotal role. This is a joint project with Tom Weston.