Math 242 -symplectic Geometry Lecture Notes

Lectures on Riemannian Geometry, Part II: Complex Manifolds

This is a set of introductory lecture notes on the geometry of complex manifolds. It is the second part of the course on Riemannian Geometry given at the MRI Masterclass in Mathematics, Utrecht, 2008. The first part was given by Prof. E. van den Ban, and his lectures notes can be found on the web-site of this course, http://www.math.uu.nl/people/ban/riemgeom2008/riemgeom2008.html. Topics that w...

An Introduction to Lie Groups and Symplectic Geometry

A series of nine lectures on Lie groups and symplectic This is an unofficial version of the notes and was last modified on 19 February 2003. (Mainly to correct some very bad mistakes in Lecture 8 about Kähler and hyperKähler reduction that were pointed out to me by Eugene Lerman.) Please send any comments, corrections or bug reports to the above e-mail address. Introduction These are the lectur...

Moment Maps, Pseudo-holomorphic Curves and Symplectomorphism Groups

These are the notes of a 3-lecture mini-course on some basic topics of symplectic geometry and topology, given at the XIV Fall Workshop on Geometry and Physics, September 14–16, 2005, in Bilbao, Spain, to a general mathematical audience.

Hyperkähler Geometry and the Moduli Space of Higgs Bundles

Today will be mostly preliminaries, including some complex and symplectic geometry, such as the symplectic quotient, and an introduction to Kähler and hyperkähler geometry. Over the rest of the week, we’ll discuss some examples (which are usually left implicit) such as quiver varieties, introduce the moduli space of Higgs bundles, and more. A good reference for this is Andy Neitzke’s lecture no...

Math 149, Fall 2008 Discrete Geometry Lecture Notes