Joint IAS/PU Number Theory

The theory of Euler systems, first developed by Thaine and Kolyvagin, has become a central tool for proving cases of the Birch–Swinnerton-Dyer and Bloch–Kato conjectures. Many of the known examples are inspired from automorphic period integrals that capture special values of L-functions. In this talk, I will focus on recent developments for Hilbert modular forms, their p-adic L-functions and some arithmetic consequences.