p-adic iteration of Maass-Shimura operators on nearly overconvergent modular forms

In the study of special values of L-functions and p-adic L-functions, it is often necessary to have a good theory of p-adic families of nearly holomorphic automorphic forms (nearly overconvergent forms) and the p-adic iteration of Maass--Shimura differential operators. There are several candidates for this theory in the literature, however there is usually a restriction, e.g., on the slopes of the nearly overconvergent forms or the p-adic variation of the differential operators. In this talk, I will discuss a new construction of this theory which doesn't come with the aforementioned restrictions. The construction should also generalise to other reductive groups which give rise to Shimura varieties. Joint work with Vincent Pilloni and Joaquin Rodrigues Jacinto.