Architecture for the Working Mathematician

Abstract:

Del Pezzo surfaces are classified by their degree, an integer between 1 and 9. Famous examples are those of degree 3, which are cubic surfaces in $P ^ 3$. In this talk I will focus on del Pezzo surfaces of degree 1. After briefly describing their geometry, I will talk about the set of Q-valued (rational) points on such a surface. I will show what is known about this set so far, and which questions are still open.