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 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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An introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture.
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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.
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An introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role which these ideas play in formalizing the transition between the mathematics of classical dynamics and that of quantum mechanics.