Welcome to my personal wiki!



Java Mathlets

I'm working on a Java package for mathematics visualization called Blaise. I maintain a collection of mathlets designed with the tool. My other ongoing projects are FireStorm (a Java utility library for property sheets and event handling), and BlaisePursuit (for exploring pursuit/evasion games).

I also maintain a collection of Geogebra workbooks, and a long time ago I worked on the fair division calculator with Francis Su.

Programming & Technology

I have written up a few notes on programming and technology. I also maintain a page of PGF/TikZ code snippets for drawing figures in LaTeX, and have started this wiki as a source for general help with TeX.

LINKS: I LaTeX using the MiKTeX distribution, WinEdt for editing/compiling, PGF/TikZ for figures, and Beamer for slides. I am also interested in Java programming with NetBeans, Geogebra for the classroom, wikis, and other new web technologies.

Professional Activities

I am a managing editor for Mathematica Militaris. I used to conduct the USMA Department of Mathematical Science's Problem of the Week competition. I am also a Project NExT Sun Dot, which is a wonderful professional-development program for recent mathematics PhDs.


As a graduate student, I began writing some Rough Guides to Mathematics. Right now it's mostly a collection of my notes from graduate school, but I have grand plans (and unfortunately little time) to develop it into a collection of concise summaries of mathematics courses. The best current article is probably the one on topology.


My research interests include:

  • Trace diagrams and their applications to linear algebra, invariant theory, moduli spaces, character varieties, and geometric structures;
  • Game theory and multi-agent systems, particularly the mathematics of cooperation in the context of pursuit and evasion games
  • Graph theory and its applications; Sperner's Lemma; fair division.
  • Uses of technology in the communication and teaching of mathematics.
Selected Papers & Preprints
  • "Cooperation in a Network: Agent Metrics and Cooperation Space" PDF (with Chris Arney), Proceedings of the 2010 Army Science Conference.
  • "Unshackling Linear Algebra from Linear Notation" arXiv:0910.1362 , submitted.
  • "n-Person Envy-Free Chore Division" arXiv:0909.0303 (with Francis Su), submitted.
  • "Computing SL(2,C) Central Functions with Spin Networks" arXiv:0903.2372 (see also this mathematica notebook with combinatorial recurrence implementation) (with Sean Lawton), to appear in Geometry Dedicatae.
  • "Trace Diagrams, Signed Graph Colorings, and Matrix Minors" arXiv:0903.1373 (with Steve Morse), Involve 3 (2010), 33-66.
  • "Spin Networks and SL(2,C) Character Varieties" arXiv: math.QA/0511271 (with Sean Lawton), Handbook of Teichmuller Theory Volume II (Chapter 16), 2009, Athanase Papadopoulos, ed., EMS Publishing House.
  • "Cooperation in Social Networks: Communication, Trust, and Selflessness" PDF (with Chris Arney), Proceedings of the 2008 Army Science Conference (chosen Best Paper in the Advanced Modeling and Simulation Category, and 3rd Best Paper Overall out of 845 abstract entries).
  • "Trace Diagrams, Representations, and Low-Dimensional Topology" PDF , PhD Thesis at the University of Maryland (advised by Bill Goldman), 2006.
  • "Combinatorial Proofs of a Generalized Sperner's Lemma" PDF , undergraduate thesis at Harvey Mudd College (advised by Francis Su), 2000.

See the complete list

Recent & Upcoming Talks
  • "Trace Diagrams: Unshackling Linear Algebra from Linear Notation" PDF Slides and PDF Handout , Bard College Mathematics Seminar, Nov 12, 2009.
  • "Trace Diagram Recurrences and Central Functions of SL(2,C)-Character Varieties" PDF Slides , AMS Special Session on Geometry, Algebra, and Topology of Character Varieties, JMM, Jan 8, 2009.
  • "Java Mathlets with Blaise" PPTX Slides and PDF Slides and Applets Page , JMM session on Mathlets for Teaching and Learning Mathematics, JMM, Jan 7, 2009.
  • "Cooperation in Social Networks: Communication, Trust, and Selflessness" PPTX Slides (with Chris Arney), Army Science Conference, Orlando, FL, Dec 2, 2008.
  • "Dynamic Mathematics and Pursuit-Evasion Games" PDF slides and PPTX slides and Applets Page , USMA Department of Mathematical Sciences Center for Faculty Development (Colloquium), Nov 20, 2008.
  • "Signed Graph Coloring, the Art of Linear Algebra, and a Theorem of Jacobi" PDF slides (with Steve Morse), MathFest, July 31, 2008.

See the complete list


Elisha Peterson was born in Ashland, Oregon on September 11, 1980. After a brief sojourn in Haiti, his family settled in a small California town named Oakhurst 13 miles outside Yosemite National Park.

He graduated from Yosemite High School in 1996, and was accepted to Harvey Mudd College in Claremont, CA, where students sing songs about slide rules and unicycle while juggling. He couldn’t use a slide rule, unicycle, or juggle, but did memorize 314 digits of pi to make sure he fit in. He also ran Division III cross country and track for the combined Claremont McKenna/Harvey Mudd team. During the summer, he spent one year doing research in combinatorics and fair division, and the next two in a summer program at the $\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\:\:\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\:\:\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare$ . His only memory from this time is one very brilliant flash of light, although he discovered after returning from $\blacksquare\blacksquare\blacksquare\blacksquare\:\:\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare$ that he could juggle. He was selected as a Rhodes Scholar on a December night his senior year at Harvey Mudd and consumed his first "beverage" at a cross country party later that night.

He matriculated in September 2000 to Oxford University. There he ran with the oldest and muddiest cross country club in the world, spent his early mornings rowing on the River Thames for Magdalen College, traveled in Europe, and theoretically worked on research involving knot theory, surgery, and hyperbolic volume.

In 2002 he returned to Maryland and married Jennifer, a classmate from Harvey Mudd College. The wedding did not take place in the Camp Mabry chapel in Austin as planned, one small consequence of the tragedy that occurred on his 21st birthday.

In August 2002 he began his doctoral studies at the University of Maryland. He found a mathematician scratching his head over some doodles on a chalkboard one day, and decided it would be fun to write equations using pictures so mathematicians wouldn’t recognize them. Those doodles became his PhD thesis, which was formally called “Trace Diagrams, Representations, and Low-Dimensional Topology”. As was pointed out during his thesis defense, the only low-dimensional topology in his thesis is the drawing of a pair of pants on the front cover.

After successfully typesetting and defending his PhD thesis in April of 2006, he joined the Math Department at the United States Military Academy (West Point).

He was thrilled in January 2007 to become the father of Micah Andrew Peterson. The little guy can't tell directions very well, but he seems anxious to digest calculus and does function continuously. In June 2010, Micah became a big brother to Asher Matthew Peterson, who despite his name does not reach the same volume as his brother.


The heart has its reasons which reason knows nothing thereof.Blaise Pascal

I'm a Christian because I know without a doubt that God loves me. Find out more about why I believe. I occasionally write on life with faith and science.


My family is what makes it all worthwhile. I am blessed with a beautiful and supportive wife Jennifer and two sons Micah and Asher.


When I have the time, I love to run and compete in triathlons. I enjoy camping, hiking, and being outdoors. I also give Micah shoulder rides and help him put together puzzles. Here's a fun video I put together of him taking a nap.

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