Joaquin Rodrigues Jacinto will speak on

Arithmetic families of (\varphi, \Gamma)-modules and locally analytic representations of GL_2(Q_p)

Abstract: Let A be a Q_p-affinoid algebra in the sense of Tate. We propose a p-adic Langlands correspondence in families: For a 'regular' trianguline (\varphi, \Gamma)-module of dimension 2 over the relative Robba ring R_A, we construct a locally analytic GL_2(Q_p)-representation in A-modules interpolating the 'classical' p-adic Langlands correspondence constructed by Colmez. This is joint work with Ildar Gaisin.