CS 782: An Introduction to Geometric Complexity Theory.

The course aims to introduce Geometric Complexity Theory (GCT), a particular approach to understanding computational complexity, along with the algebraic and geometric tools needed. The basic preparation which is required as a prerequisite is basic group theory, linear alegbra and commutative algebra and some rudimentary notions of ideals and varieties. Most of this will be reviewed through examples which lie on the GCT path. We will use some standard books: Humphreys, for Algebraic Groups, Harris for Algebraic Geometry and others as and when needed. These are NOT prerequisites. We will also be reading research papers. The class will meet twice a week, for the initial few weeks.

Familiarity required: Linear Algebra, Basic Algebra, Commutative algebra, Groups and group actions, group representation, ideals and varieties. Artin's Algebra is adequate.

  • Detailed Course contents pdf
  • Lecture topics and notes pdf

    • Some reference books:

  • Kunze, Algebraic Geometry and Commutative Algebra pdf
  • Sturmfels, Algorithms in Invariant Theory pdf
  • Humphreys, Algebraic Groups pdf
  • Harris, Algebraic Geometry pdf
  • Derksen, Constructive Invariant Theory pdf