Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
by Vincent Bouchard
Publisher: arXiv 2007
Number of pages: 63
These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds. The last section provides a short introduction to toric geometry.
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by Richard S. Palais - University of California at Irvine
The major goal of these notes is to develop an observation that not only can gauge fields of the Yang-Mills type be unified with the Einstein model of gravitation, but also that when this unification is made they are described by pure geometry.
by Alexander Altland
Contents: Exterior Calculus (Exterior Algebra, Differential forms in Rn, Metric, Gauge theory); Manifolds (Basic structures, Tangent space); Lie groups (Lie group actions, Lie algebras, Lie algebra actions, From Lie algebras to Lie groups).
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These are the lecture notes from a graduate course in the geometry of quantum mechanics. The idea was to introduce the mathematics in its own right, but not to introduce anything that is not directly relevant to the subject.
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These lectures notes are an introduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists.