On P vs. NP, Geometric Complexity Theory, and the Riemann Hypothesis

Geometric complexity theory (GCT) is an approach to the P vs. NP and related problems suggested in a series of articles we call GCTlocal [27], GCT1-8 [30]-[35], and GCTflip [28]. A high level overview of this research plan and the results obtained so far was presented in a series of three lectures in the Institute of Advanced study, Princeton, Feb 9-11, 2009. This article contains the material covered in those lectures after some revision, and gives a mathematical overview of GCT. No background in algebraic geometry, representation theory or quantum groups is assumed. For those who are interested in a short mathematical overview, the first lecture (chapter) of this article gives this. The video lectures for this series are available at: http://video.ias.edu/csdm/pvsnp They may be a helpful supplement to this article.