The Grothendieck ring of varieties is defined as the set of equivalence classes of varieties, modulo a natural equivalence relation; despite this simple description, it's a very complicated ring, but one worth studying: it has applications to stably birational geometry, motivic integration and Kapranov's motivic zeta function, and Kontevich's proof of the birational invariance of Hodge numbers of smooth projective varieties. In this talk, we'll define the Grothendieck ring of varieties and explore a few of its basic properties (e.g., it fails to be a domain or even reduced in characteristic 0). We'll do some example calculations in this ring and define several important homomorphisms from this ring (i.e., "motivic invariants"). We'll then state and sketch a theorem of Larsen and Luntz relating these ideas to stably birational geometry, and finally we'll hopefully mention some broader applications to motivic integration and birational geometry. No background beyond basic algebraic geometry will be assumed. Speaker(s): Devlin Mallory (UM)