In the previous talk, we introduced the notion of geometric modularity in the sense that $\rho$ arises from a mod $p$ Hilbert modular form, and algebraic modularity in the sense that $\rho$ arises in the mod $p$ cohomology of a Shimura curve. In this talk, I will explain the idea of the proof that geometric modularity implies algebraic modularity of the same weight. The main strategies are the liftability of mod p Hilbert cusp forms, using weight-shifting operators, and the description of the Goren-Oort stratification.