Title: Geometry of algebraic surfaces via their Cox rings

Abstract: Cox ring is an important tool in modern algebraic geometry and several other branches of mathematics. In the first part of this talk, I will briefly review basic theory of Cox ring and explain how it connects birational geometry and geometric invariant theory. Then I will discuss how we can use Cox rings to study geometry of certain algebraic surfaces. This talk is based on several joint works (some in progress) with JongHae Keum and Davide Frapporti.