Kyoung-Seog Lee, Cox Rings and Geometry of Some Surfaces of General Type with p_g=q=0

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 of general type with p_g=q=0. The second part of this talk is based on several joint works (some in progress) with JongHae Keum and Davide Frapporti.