Classicality of overconvergent Hilbert modular forms and related topics

The classicality of overconvergent Hilbert modular forms can be proved in two ways: the approach of analytic continuation and that of p-adic cohomology. In this talk, I will give a summary on  my work in both directions. In the cohomological approach, an important role is played by an interesting description on the global geometry of Goren-Oort strata of Hilbert modular varieties in characteristic p.