# TR-2007-16

## Geometric Complexity Theory: Introduction

Ketan D. Mulmuley; Milind Sohoni. 4 September, 2007.

Communicated by Ketan Mulmuley.

**Obsolete:** Yes *(updated 12/19/12)*

### Abstract

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.

### Original Document

The original document is available in Postscript (uploaded 4 September, 2007 by
Ketan Mulmuley).