Back-To-School Seminar: The Brauer-Manin obstruction on del Pezzo surfaces of degree 2.

When looking for rational points on varieties, we can often disprove the existence of solutions by checking various positivity or modular arithmetic conditions.  However, even if we pass all of these checks, we could still fail to have rational points! In this talk, we'll explore the Brauer-Manin obstruction as a way to explain the absence of rational points.  We'll also discuss my ongoing project to prove the local-to-global principle of certain special del Pezzo surfaces of degree 2.