The use of modular symbols to attach p-adic Lfunctions to Hecke eigenforms goes back to the work of Manin et al in the 70s.
We will start looking at the second part of “L-functions and Euler systems: a tale in two trilogies” (available at http://www.math.mcgill.ca/darmon/pub/Articles/Research/61.Durham-ES/durham.pdf), and distributing talks.
I will explain A.Lauder’s approach to computing special values of Rankin triple product p-adic L-functions. These have quite striking applications to the arithmetic of elliptic curves, and appear in the “Elliptic Stark Conjecture” of Darmon-Lauder-Rotger.
Second talk of the learning seminar on the Tale on 2 trilogies.