Algebraic Geometry

This course is an introduction to algebraic geometry. Algebraic geometry is the study of zero sets of polynomials. It exploits the interplay between rings of functions and the underlying geometric objects on which they are defined. It is a fundamental tool in may areas of mathematics, including number theory, physics and differential geometry. The syllabus will cover affine and projective varieties, the Nullstellensatz, Zariski topology, morphisms, sheaves, schemes and may include additional topics in algebra and algebraic geometry (e.g., dimension, smoothness, singularities).