Certain constructions of p-adic families of Siegel modular forms and their applications

As an affirmative answer to the Duke-Imamoglu conjecture concerning a
generalization of the Saito-Kurokawa lifting in the case of higher genus, Ikeda
constructed a Langlands lifting from elliptic modular forms of level 1 to Siegel
modular forms of even genus and of level 1. In this talk, we would like to
introduce a similar lifting of Hida's p-adic analytic families of elliptic
modular forms to those of Siegel modular forms of arbitrary even genus. As a
consequence, we may also construct a classical lifting of ordinary elliptic
modular forms of p-power level to Siegel modular forms of $p$-power level.