Geometric Complexity Theory: Introduction
arXiv:0709.0746
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 \cite{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.
161 pages
References in corpus (4)
- Geometric Complexity Theory VI: the flip via saturated and positive integer programming in representation theory and algebraic geometry
- Geometric Proofs of Horn and Saturation Conjectures
- Geometric Complexity Theory V: On deciding nonvanishing of a generalized Littlewood-Richardson coefficient
- An Invitation to the Generalized Saturation Conjecture