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Geometry and Topology in Electronic Structure TheoryGeometry and Topology in Electronic Structure Theory
by Raffaele Resta - University of Trieste , 2012
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.
(2141 views)

First Steps Towards a Symplectic DynamicsFirst Steps Towards a Symplectic Dynamics
by Barney Bramham, Helmut Hofer - arXiv , 2011
Both dynamical systems and symplectic geometry have rich theories and the time seems ripe to develop the common core with integrated ideas from both fields. We discuss problems which show how dynamical systems and symplectic ideas come together.
(3540 views)

Topology and Physics: A Historical EssayTopology and Physics: A Historical Essay
by C. Nash - arXiv , 1997
In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
(4932 views)

Geometry, Topology and PhysicsGeometry, Topology and Physics
by Maximilian Kreuzer - Technische Universitat Wien , 2010
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.
(6409 views)

Edinburgh Lectures on Geometry, Analysis and PhysicsEdinburgh Lectures on Geometry, Analysis and Physics
by Michael Atiyah - arXiv , 2010
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.
(2599 views)

Geometry in PhysicsGeometry in Physics
by Alexander Altland , 2010
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).
(3695 views)

Geometry and Group TheoryGeometry and Group Theory
by Christopher Pope - Texas A&M University , 2008
Lecture notes on Geometry and Group Theory. In this course, we develop the basic notions of Manifolds and Geometry, with applications in physics, and also we develop the basic notions of the theory of Lie Groups, and their applications in physics.
(7779 views)

Lectures on Calabi-Yau and Special Lagrangian GeometryLectures on Calabi-Yau and Special Lagrangian Geometry
by Dominic Joyce - arXiv , 2002
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.
(3993 views)

Lectures on complex geometry, Calabi-Yau manifolds and toric geometryLectures on complex geometry, Calabi-Yau manifolds and toric geometry
by Vincent Bouchard - arXiv , 2007
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.
(2585 views)

Introduction to Braided Geometry and q-Minkowski SpaceIntroduction to Braided Geometry and q-Minkowski Space
by Shahn Majid - arXiv , 1994
Systematic introduction to the geometry of linear braided spaces. These are versions of Rn in which the coordinates xi have braid-statistics described by an R-matrix. From this starting point we survey the author's braided-approach to q-deformation.
(2235 views)

An Introduction to Noncommutative Spaces and their GeometryAn Introduction to Noncommutative Spaces and their Geometry
by Giovanni Landi - arXiv , 1997
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.
(4396 views)

Noncommutative Geometry, Quantum Fields and MotivesNoncommutative Geometry, Quantum Fields and Motives
by Alain Connes, Matilde Marcolli - American Mathematical Society , 2007
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.
(4106 views)

Noncommutative GeometryNoncommutative Geometry
by Alain Connes - Academic Press , 1994
The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.
(4726 views)

Geometry of Quantum MechanicsGeometry of Quantum Mechanics
by Ingemar Bengtsson - Stockholms universitet, Fysikum , 1998
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.
(5730 views)

The Geometrization of PhysicsThe Geometrization of Physics
by Richard S. Palais - University of California at Irvine , 1981
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.
(4914 views)

Lectures on the Geometry of QuantizationLectures on the Geometry of Quantization
by Sean Bates, Alan Weinstein - University of California at Berkeley , 1997
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.
(5157 views)

Differential Geometry in PhysicsDifferential Geometry in Physics
by Gabriel Lugo - University of North Carolina at Wilmington , 2006
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.
(8847 views)