in Texas.
They both attend Mountaintop Doggy Days.
I've worked in a number of areas over time of which equivariant
differential geometry and dynamical systems are of greatest current interest.
Other areas of past work include transformation groups, homotopy theory,
geometric modeling and robotics.
Notes and Expositions
- Smith Theory by Example V7
- A beamer pdf highlighting the algorithmic nature of the
Wu-Yi Hsiang approach to Smith theory via equivariant cohomology.
- My Ph. D. thesis was an intense example of this.
- Kobayashi-Nomizu Differential Geometric Conventions
- I spent my first year in grad school reading both volumes, so have
had some version of these around for almost 40 years.
- Nowadays, I mostly end up needing to reconcile these with those of Besse
and Peterson.
- Integration by Parts V2 dg_cao_v2.pdf
- Having marveled for decades at how less effective some of my instinctive
preferences for styles of diff geo calculation are at integration by parts than those of people like
Richard Hamilton (and more recently Xiaodong Cao), I wrote some of these down.
- Notes from Cartan for Beginners
- Cartan for Beginners is a very accessible introduction to exterior differential systems.
- A Quadratic Vector Field on $R^3$ with an Unstable Manifold which is exactly the graph of a quadratic function.
- A good test example (both experimental and theoretical) for
stable manifold computation algorithms.
Below is a list of papers:
- Review of the Movie
Hard Problems. The Road to the
World's Toughest Math Contest American Statistician,
Volume 63 (2009) 192-193.
(Electronic copy is part of the Review of Books and Teaching Materials.)
- A Transformation Groups Point of View on Connelly's
Global Rigidity Theorem for Free Equivariant Tensegrities
(with Robert Connelly) (2007).
- Runge Kutta Behavior in the Presence of a Jump
Discontinuity (2005).
- Inverting a Batting Average - an Application of Continued Fractions (2000). (A small observation perhaps
obvious to anyone who knows the theory of continued fractions.)
- Mathematics and Tensegrity (with Robert Connelly)
American Scientist , Volume 86 (1998) 142-151.
- From Instantaneous Motion to Task-Directed
Constrained Manipulation (with Daniela Rus)
IEEE Intelligent Robots and Systems
Volume 3 (1993) 1598 - 1605.
- dstool: Computer Assisted Exploration of Dynamical
Systems (with J. Guckenheimer, M. Myers, F.J.
Wicklin, and P. Worfolk), Notices of the American
Mathematical Society 39 (1992) 303 - 309.
- A Dynamical Simulation Facility for Hybrid
Systems (1992)
(with John Guckenheimer and Mark Myers), in
Lecture Notes in Computer Science 736, Hybrid
Systems edited by Robert L. Grossamn, et. al.,
Springer Verlag, Berlin, 1993.
- Systematic Conversion of Boundary Integral Surface
Integrals to Contour Integrals (1992),
(with E.D.Lutz, L.G.Gray, and A.R.Ingraffea), Cornell
Department of Civil And Environmental Engineering
Report 92-6.
- Solid Quality Norms and Consistency Strategies in
Robust Intersection of Simplicial Complexes (1990).
- Local Theory of Equivariant Einstein Metrics and Ricci
Realizability on Kervaire Spheres (1986).
- Kervaire Spheres and Equivariant Geometry (with
Wu - Yi Hsiang), Transactions American Mathematical
Society 304 (1987) 207 - 227. JSTOR Version
- Fundamental Equations in Equivariant Geometry (with Manfredo
do Carmo and Wu - Yi Hsiang) BdCH.pdf(1984).
- Pontryagin Forms on Homogeneous Spaces, Commentari Mathematica Helvetica 57 (1982) 349 - 355.
GDZ persistent URL
- Rational Pontryagin Classes and Killing Forms, Journal of Differential Geometry 16 (1981) 191 - 193. JDG Archive Version
- Homotopy Rigidity For Grassmanians, Proceedings
American Mathematical Society 80 (1980) 327 - 332.
JSTOR Version
-
New Gravitational Instantons and Universal Spin Structures
(with P. Freund and M. Forger), Physics Letters 77B
(1978) 181 - 184.
- Involutions on Grassman Manifolds, Ph. D. Thesis, Berkeley 1977.
Many of the web pages I have edited are at the former
