Explicit Arithmetic on Algebraic Surfaces
Anthony Várilly-Alvarado, Rice University

The geometric complexity of a variety is a good proxy for its arithmetic complexity. Using the classification of algebraic surfaces as a guide for geometric complexity, we will discuss explicit techniques for computing cohomological obstructions to the existence and distribution of rational points on algebraic surfaces, with a view toward identifying a boundary between arithmetically ``well-behaved'' varieties, like rational surfaces, and arithmetically ``wild'' varieties, like surfaces of general type.