del Pezzo surfaces are a special class of surfaces, they are those which have an ample anticanonical bundle. These surfaces have a satisfactory classification, in fact every del Pezzo surface is either a blowup of P^2 at < 9 points or P^1 \times P^1. I plan to discuss some basic properties of these surfaces and then explain in some detail their classification. A good portion of the talk (if not the whole talk!) will be accessible to anyone currently taking Math 632. Speaker(s): Sridhar Venkatesh (UM)