Unfolded irregular icosahedron

Math 537B Spring 2012

Room/Time: Tuesday, Thursday 12:30-1:45 in Shantz 242W
Instructor: David Glickenstein
Office: Mathematics 715
Office Phone: 621-2463
Office Hours: I will be available after class, or feel free to stop by my office or make an appointment
Email: glickenstein@math.arizona.edu

Printed resources

This semester we will use an eclectic mix of sources, including:

Ricci Flow: An Introduction by Ben Chow and Dan Knopf
T. Tao's blog on the Poincare Conjecture.
Riemannian Geometry by Peter Petersen
Foundations of Differentiable Manifolds and Lie Groups, by Frank W. Warner

Lecture notes

These lecture notes are not particularly well edited and not for general distribution, which is why the files are password protected.

Structure of 2D and 3D manifolds
Ricci flow on surfaces. Last updated February 7, 2012
Hodge Theory. Last updated March 2, 2012
The Hopf fibration and 3D Lie groups. Last updated March 27, 2012.
Convergence of Riemannian manifolds and applications. Last updated April 24, 2012.
Discrete conformal geometry (slides).

Math 537A Fall 2011

Room/Time: Tuesday, Thursday 12:30-1:45 in Math East 246
Instructor: David Glickenstein
Office: Mathematics 715
Office Phone: 621-2463
Office Hours: Monday 2-3 (in Math East 145), Tuesday 2-3 (in Math 715), Wednesday 10:30-11:30 (in Math 715)
Email: glickenstein@math.arizona.edu

Syllabus

The syllabus is available here.

Printed resources

The books we are currently using are:

Riemannian Manifolds: An Introduction to Curvature by John Lee. He has errata here.

Other books of note:

Elementary Differential Geometry Lecture Notes by Gilbert Weinstein.
Riemannian Geometry by M. P. Do Carmo
A Comprehensive Introduction to Differential Geometry by M. Spivak
Riemannian Geometry: A Modern Introduction by I. Chavel
Lectures on Differential Geometry by R. Schoen and S. T. Yau
Comparison Theorems in Riemannian Geometry by J. Cheeger and D. Ebin
Riemannian Geometry by Peter Petersen

Homework assignments

Lecture notes

These lecture notes are not particularly well edited and not for general distribution, which is why the files are password protected.

Notes from when I taught this class 2005-2006
Notes from when I taught this class 2007-2008.
Curves. Last updated August 22, 2011

Projects

Introduction to symplectic geometry - Angel
Existence of ODE - Shane
Plateau's problem - Joe

Possible project topics

Existence of convex neighborhoods of points.
First variation of area and minimal surfaces
Formulation of geodesic equation as a Hamiltonian system
Derivatives of the Riemannian distance function
Thurston's 3D model geometries
Hodge theorem
Trigonometry on the sphere and hyperbolic space
Areas of spherical triangles and hyperbolic triangles
Geodesics on manifolds of revolution
Examples of homogeneous spaces
Isoperimetric inequality
The existence of a triangulation on any surface
Whitney's classification of surfaces

Last updated April 30, 2012