Notes
- Instantons and Self-Dual Gauge Fields [ ps | pdf ]
- An essay prepared as a final project in Dan Freed's course on the Atiyah-Singer index theorem during Spring 2004. Last updated: 2004-5-11.
- Manifolds with G2 Holonomy [ ps | pdf ]
- An essay prepared as a final project in Tamás Hausel's Riemannian Geometry course at UT during Fall 2003. Last updated: 2003-12-5.
- Worldsheets, Riemann Surfaces, and Moduli [ ps | pdf ]
- Notes from a lecture I gave to our string theory study group. The final section on Klein surfaces is still incomplete. Last updated: 2003-10-13.
- Orbifolds [ ps | pdf ]
- A review of orbifolds in conformal field theory and string theory. Prepared as a final project in Jacques Distler's string theory course (PHY 396P/Q) at UT during Spring 2002. Coauthored with Rick Hankins. Last updated: 2002-5-3.
- String Theory [ ps | pdf ]
- A very incomplete set of lecture notes taken from Jacques Distler's string theory course (PHY 396P/Q) at UT during Fall 2001. I intended to TeX up all the notes, but I never got around to finishing them. Last updated: 2003-12-6.
Mathematica Packages
If you use Mathematica long enough you start reusing the same custom functions enough that it becomes convenient to put them in packages that you can load at will. And so your own little library is born. For anyone who is interested I have posted mine below. These packages are in various disarrays of maturity. Many are undocumented and untested, some are more polised. Hopefully all are more or less self-explanatory. Use them as you see fit.
Note: To install these files create
a subdirectory of your personal Applications directory (see the
Mathematica documentation) called JOlson and place the
files in there. To load a particular package in Mathematica issue a
command like the following:
<<JOlson`ComplexPlot`
For convenience you may download the entire set as a
gzipped tar file.
| Package | Date | Description |
|---|---|---|
| General | ||
| Bessel | 2003-1-14 | Definitions for spherical Bessel functions as well as Hankel functions. |
| Common | 2003-1-14 | Some simple functions for use in functional programming as well as aliases for common system functions. |
| Fourier | 2003-1-14 | Provides separate definitions of Fourier transforms for space and time dimensions consistent with the signature of Minkowski spacetime. Also allows one to show the kernel used with a given transform. |
| Gaussian | 2003-1-14 | Provides definitions for normalized and square-normalized Gaussian wave packets. |
| Roots | 2003-1-14 | Alternative methods for finding roots of equations. Mathematica sometimes has trouble with the obvious. |
| Young Tableaux | 2003-1-14 | Provides functions for dealing with Young tableux and partitions of integers. |
| Graphics | ||
| Color | 2003-1-14 | Provides definitions of basic colors, functions for dealing with color primatives, and functions for producing basic color charts. |
| Complex Plot | 2003-1-14 | Provides various methods for plotting functions of a complex variable. Includes the functions implemented in Graphics`ComplexMap`. |
| Graphic Objects | 2003-1-14 | Graphics primatives for drawing Cartesian, polar, and triangular grids. |
| Surfaces | 2003-1-14 | Provides common parameterizations for immersions of two dimension manifolds in three dimensional space. |
| Group Theory and Algebra | ||
| Classical Groups | 2003-1-14 | Provides matrix representations for some common classical groups/algebras as well as matrix exp maps from Lie algrebras to the associated Lie groups. |
| Lorentz Group | 2003-1-26 | Extends the definitions in ClassicalGroups to include the Lorentz group. |
| Matrix Algebra | 2003-1-14 | Common functions for dealing with matrices and linear transformations. |
| Spin Matrices | 2003-1-26 | Provides definitions for the Pauli spin matrices and the Dirac gamma matrices. Also defines matrix representations for the Clifford algebras Cl(3) and Cl(1,3). |
| Units and Constants | ||
| CODATA 1998 | 2003-1-14 | Implements the 1998 CODATA recommended values for the fundamental physical constants. |