The next lecture in this series is here.
The classification of algebraic varieties is at the heart of algebraic geometry. With roots in the ancient world the theory saw great advances in dimensions one and two in the 19th century and the first half of 20th century. It was only in the 1970-80s that a general framework was formulated, and by the early 1990s a satisfactory theory was developed in dimension 3. The last 30 years has seen great progress in all dimensions.
In the first lecture I will try to give a historical perspective and discuss the theory in general terms. I will explain how the theory is based on birational transformations and moduli considerations.
This video was produced by the Japan-US Mathematics Institute and forms part of the Monroe H. Martin Lectures.