Lectures on the Geometry of Quantization
by Sean Bates, Alan Weinstein
Publisher: University of California at Berkeley 1997
Number of pages: 134
This is 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 (hamiltonian flows on symplectic manifolds) and that of quantum mechanics (unitary flows on Hilbert spaces).
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by Vincent Bouchard - arXiv
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.
by Alain Connes, Matilde Marcolli - American Mathematical Society
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.
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.
by Christopher Pope - Texas A&M University
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.