Upper bounds for constant slope padic families of modular forms
Upper bounds for constant slope padic families of modular forms

John Bergdall (Bryn Mawr)
IAS  Simonyi Hall Seminar Room SH101
This talk is concerned with the radius of convergence of padic families of modular forms  qseries over a padic disc whose specialization to certain integer points is the qexpansion of a classical Hecke eigenform of level p. Numerical experiments by Gouvêa and Mazur in the nineties predicted the general existence of such families but also suggested, in spirit, the radius of convergence in terms of an initial member. Buzzard and Calegari showed, ten years later, that the GouvêaMazur prediction was false. It has since remained open question how to salvage it. Here we will present some recent theoretical results towards such a salvage, backed up by numerical data.