Geometric Complexity Theory: An Introduction for Geometers
by J.M. Landsberg
Publisher: arXiv 2013
Number of pages: 38
This is survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT). The article is written to be accessible to graduate students. Numerous open questions in algebraic geometry and representation theory relevant for GCT are presented.
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Basic concepts of complex geometry, coherent sheaves and complex analytic spaces, positive currents and potential theory, sheaf cohomology and spectral sequences, Hermitian vector bundles, Hodge theory, positive vector bundles, etc.
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