Title: Deformation Theory and Galois Representations
Speaker: Eknath Ghate, Tata Institute of Fundamental Research
Abstract: Unlike the global Galois representation attached to an ordinary newform of weight at least two, the associated local representation is reducible. Greenberg has asked whether it is semi-simple.

In the CM-case, this is known to be true, but the non-CM case is much more mysterious.

Using the deformation theoretic methods of Mazur we will give the first non-trivial examples of non-CM Hida families where no weight 2 or more member has a semi-simple representation.

This is a continuation of earlier joint work with Vatsal.