Optimization Algorithms on Matrix Manifolds
by P.-A. Absil, R. Mahony, R. Sepulchre
Publisher: Princeton University Press 2007
Number of pages: 240
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis.
Home page url
Download or read it online for free here:
(multiple PDF files)
by John Douglas Moore - Springer
A streamlined introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure.
by Ville Turunen - Aalto TKK
In this book you will learn something about functional analytic framework of topology. And you will get an access to more advanced literature on non-commutative geometry, a quite recent topic in mathematics and mathematical physics.
by C.H. Dowker - Tata Institute of Fundamental Research
A sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. Contents: Sheaves; Sections; Cohomology groups of a space with coefficients in a presheaf; Introduction of the family Phi; etc.
by David Ellwood, at al. - American Mathematical Society
Mathematical gauge theory studies connections on principal bundles. The book provides an introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds.