Geometry and Topology in Electronic Structure Theory
by Raffaele Resta
Publisher: University of Trieste 2012
Number of pages: 83
From the table of contents: Introduction; Early discoveries; Berry-ology (geometry in nonrelativistic quantum mechanics); Manifestations of the Berry phase; Modern theory of polarization; Quantum metric and the theory of the insulating state.
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by Maximilian Kreuzer - Technische Universitat Wien
From the table of contents: Topology (Homotopy, Manifolds, Surfaces, Homology, Intersection numbers and the mapping class group); Differentiable manifolds; Riemannian geometry; Vector bundles; Lie algebras and representations; Complex manifolds.
by Michael Atiyah - arXiv
These notes are based on a set of six lectures that the author gave in Edinburgh and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and they may stimulate readers to investigate them.
by Sean Bates, Alan Weinstein - University of California at Berkeley
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.
by Gabriel Lugo - University of North Carolina at Wilmington
These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.