Modular forms, congruences, and applications

One approach to studying the p-adic behavior of L-functions relies on understanding p-adic properties of certain modular forms. In this talk, I will discuss an approach to studying these properties, and I will introduce a construction of certain p-adic families of modular forms. As part of the talk, I will explain how this construction allows one to p-adically interpolate certain values of both holomorphic and non-holomorphic Eisenstein series. I will also mention some applications to number theory and beyond.Non UBCUnreviewedAuthor affiliation: University of OregonFacult