Dichotomies in Ontology-Mediated Querying with the Guarded Fragment

I'll talk a bit about P/NP dichotomies for various problems and
the Feder-Vardi conjecture (to which three "solutions" have been
presented in the past three months - none of them has been confirmed correct).
Then I'll talk about recent work on dichotomies in OBDA with the
guarded fragment which is closely related to the Feder-Vardi conjecture.