Diagonal restrictions of Hilbert Eisenstein series.
This last lecture explains how the diagonal restrictions of the p-adic family of
Hilbert modular Eisenstein series for a real quadratic field can be related to
RM values of certain rigid analytic cocycles, leading to an interpretation of
Gross-Stark units and Stark-Heegner points as triple product periods. The
p-adic deformation theory of the weight one Hilbert Eisenstein series, building on the
work of Bellaiche-Dimitrov, Darmon-Lauder-Rotger, and Betina-Dimitrov Pozzi,
is a key ingredient in some of the most important arithmetic applications.