MMP has found many applications since then in algebraic geometry, as well as in other fields. It has shed new light onto known results and even gave a better understanding of the classical theory of minimal models of surfaces. New classes of singularities that were originally introduced as a necessity have appeared to play important roles in many other parts of algebraic geometry and other fields of mathematics, such as commutative algebra and string theory. An operation called "flop," originally developed within the MMP, has found a significant role in the mathematical side of string theory.

In this course, I will briefly review the theory of minimal models of algebraic surfaces, why it was believed that it would not exist for hight dimensional varieties, and why this belief was later overturned. Then, I will discuss the foundations of MMP, the role vanishing theorems play in it, and the definition and importance of "flips" and "flops." Time permitting, I will also mention recent developments and applications of the theory.

Text: Birational geometry of algebraic varieties by Kollár-Mori.

Prerequisites: Basic knowledge of algebraic geometry on the level of 507/8.