Wednesday, April 12
Milner 317, 12:30 PM
Title: Rational points on del Pezzo surfaces
Abstract: Algebraic geometers are interested in complex solutions to polynomial equations, while number theorists are interested in rational solutions to polynomial equations. When there are infinitely many rational solutions, it is natural to try to count the number of points whose size is bounded in some reasonable way (by using height functions) and to study whether the rational solutions are equidistributed in a suitable sense (by using a certain adelic measure). We will discuss these issues for del Pezzo surfaces, surveying the recent results as well as the open problems in this area.