p-adic Langlands' Transfer

Abstract : The general philosophy of Langlands' functoriality predicts that given two groups H and G, if there exists a 'nice' map between the respective L-groups of H and G then using the map we can transfer automorphic representations of H to that of G. Few examples of such transfers are Jacquet-Langlands' transfer, endoscopic transfer and base change. On the other hand, by the work of Serre, Hida, Coleman, Mazur and many other mathematicians, we can now construct p-adic families of automorphic forms for various groups. In this talk, we will discuss some examples of Langlands' transfers which can be p-adically interpolated to give rise to maps between appropriate p-adic families of automorphic forms.