21th Feb: James Kiln

Title: The Coleman-Mazur Eigencurve 

Abstract: The theory of p-adic modular forms and their relation to representations of certain Galois groups is a huge area of interest in modern number theory. The 1998 paper of Coleman and Mazur titled "The Eigencurve" brings together a large collection of results in non-archimedean analysis, Galois deformation theory and p-adic modular forms to construct a rigid analytic space whose C_p points parameterise the space of all finite slope overconvergent p-adic modular forms of tame level 1 with Fourier coefficients in C_p. In this talk I will outline Coleman and Mazur's construction of the eigencurve and mention why it is an object of such interest.