We discuss non-vanishing modulo p of special values of L-functions in Iwasawa theoretic families. This includes the case of Dirichlet L-functions and Hecke L-functions over a CM field. The latter is based on Hida's pioneering work relying on Chai's theory of Hecke stable subvarieties of a mod p Shimura variety. If time permits, we discuss subsequent developments.
Session II, Tuesday 12 September.
Session III, Thursday 14 September.