Topological modular forms (aftern Hopkins, Miller, and Lurie)

This is the companion article to the Bourbaki talk of the same name given in March 2009. The main theme of the talk and the article is to explain the interplay between homotopy theory and algebraic geometry through the Hopkins-Miller-Lurie theorem on topological modular forms, from which we learn that the Deligne-Mumford moduli stack for elliptic curves is canonically realized as an object in derived algebraic geometry.