First Steps Towards a Symplectic Dynamics
by Barney Bramham, Helmut Hofer
Publisher: arXiv 2011
Number of pages: 60
Both the field of dynamical systems and the field of symplectic geometry have rich theories and the time seems ripe to develop the common core with highly integrated ideas from both fields. We discuss problems which show how dynamical systems questions and symplectic ideas come together in a nontrivial way.
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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 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 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 Richard S. Palais - University of California at Irvine
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.