Geometric Complexity Theory: Introduction

Foreword These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author in the spring quarter, 2007. It gives introduction to the basic structure of GCT. Part II consists of the lecture notes for the course given by the second author in the spring quarter, 2003. It gives introduction to invariant theory with a view towards GCT. No background in algebraic geometry or representation theory is assumed. These lecture notes in conjunction with the article [GCTflip1], which describes in detail the basic plan of GCT based on the principle called the flip, should provide a high level picture of GCT assuming familiarity with only basic notions of algebra, such as groups, rings, fields etc. Many of the theorems in these lecture notes are stated without proofs, but after giving enough motivation so that they can be taken on faith. For the readers interested in further study, Figure 1 shows logical dependence among the various papers of GCT and a suggested reading sequence. for taking notes for his lectures.