Elisha Peterson's Publications and Talks

As of 2010, this page is no longer being maintained.

Paper/Talk Tags:

accepted accessible altruism blaise calculus cas catpursuit cattech cattrace central-functions characteristic-equation character-varieties chris-arney combinatorics cooperation cooperative-systems determinants diagrams dodgson-condensation fair-division featured fixed-points game-theory geogebra in-progress invariant-theory invited java lagrange-multipliers linear-algebera linear-algebra lucas-gebhart mathematics-education mathlets multi-agent-systems multivariable network-science nj-symbols online optimization photography proceedings published pursuit-evasion real-analysis recurrence representation-theory selflessness sl2c social-networks

Paper/Talk Pages by Date:

• 2010 (7)
  • December (1)
  • April (6)
• 2009 (13)
  • November (5)
  • October (1)
  • September (2)
  • August (1)
  • July (3)
  • March (1)
• 2008 (31)
  • December (17)
  • September (14)

Scholarly Papers and Other Written Work

[arXiv search]

Theses

• "Trace Diagrams, Representations, and Low-Dimensional Topology" , PhD Thesis at the University of Maryland (advised by Bill Goldman), 2006. PDF
• "Combinatorial Proofs of a Generalized Sperner's Lemma" , undergraduate thesis at Harvey Mudd College (advised by Francis Su), 2000. PDF

Journal Articles and Book Chapters

• "Computing SL(2,C) Central Functions with Spin Networks" (with Sean Lawton), to appear in Geometry Dedicatae. arXiv:0903.2372 (see also this mathematica notebook with combinatorial recurrence implementation)
• "Trace Diagrams, Signed Graph Colorings, and Matrix Minors" (with Steve Morse), Involve 3 (2010), 33-66. arXiv:0903.1373
• "Using a Wiki to Enhance Cooperative Learning in a Real Analysis Course" , PRIMUS 19, pp. 18-28, 2009. journal link
• "Spin Networks and SL(2,C) Character Varieties" (with Sean Lawton), Handbook of Teichmuller Theory Volume II (Chapter 16), 2009, Athanase Papadopoulos, ed., EMS Publishing House. arXiv: math.QA/0511271
• "Four-person envy-free chore division" (with Francis Su), Mathematics Magazine 75, pp. 117-122, 2002. PDF
• "A polytopal generalization of Sperner's Lemma" (with Francis Su & Jesus de Loera), Journal of Combinatorial Theory Series A 100, pp. 1-26, 2002. PDF

Refereed Conference Proceedings

• "Cooperation in a Network: Agent Metrics and Cooperation Space" (with Chris Arney), Proceedings of the 2010 Army Science Conference. PDF
• "Cooperation in Social Networks: Communication, Trust, and Selflessness" (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). PDF

Works under Review

• "Unshackling Linear Algebra from Linear Notation" , submitted. arXiv:0910.1362
• "On a Diagrammatic Proof of the Cayley-Hamilton Theorem" , submitted. arXiv:0907.2364
• "n-Person Envy-Free Chore Division" (with Francis Su), submitted. arXiv:0909.0303

Technical Reports & Unpublished Expository Work

• "Subset Team Games and Cooperation Space: Theory and Application" , technical report for the 2009 ARL-USMA Technical Symposium, Atlantic City, NJ.
• "Cooperation in a Network: Theoretical Considerations" (with Chris Arney), technical report for the 2009 USMA Network Science Workshop, West Point, NY.
• "Cooperation in a Network: Altruism increases Flow" (with Chris Arney), technical report for the 2009 USMA Network Science Workshop, West Point, NY.
• "Dynamic Cobwebbing with Geogebra" , online tutorial, 2008. link
• "A mathematical formalism for selfish and altruistic cooperation in social networks" (with Chris Arney), technical report for the 2007 USMA Network Science Workshop, West Point, NY. PDF
• "A Not-so-Characteristic Equation: the Art of Linear Algebra" , unpublished expository article, 2008. arXiv:0712.2058

In Progress

• "Trace Diagrams and the Invariant Theory of 2x2 Matrices" , in preparation.
• "Generalized Trace Diagram Recurrences and the Computation of nj-Symbols" , in preparation.
• "Cooperation in Subset Team Games: Altruism and Selfishness" , preprint. arXiv:0907.2376

Talks since 2006

Trace Diagrams, Character Varieties, and Applications

• "Unshackling Linear Algebra from Linear Notation" , Davidson College Math Coffee, Feb. 9, 2010.
• "Trace Diagrams and their Applications" , Olin College Research Seminar, Feb. 5, 2010.
• "Trace Diagrams: Unshackling Linear Algebra from “Linear” Notation" , general contributed paper session, JMM, Jan 15, 2010.
• "Trace Diagrams: Unshackling Linear Algebra from Linear Notation" , Bard College Mathematics Seminar, Nov 12, 2009. PDF Slides and PDF Handout
• "Unshackling Linear Algebra from Linear Notation" , USMA Math Department Research Seminar, Sep 9, 2009. PDF Slides
• "Trace Diagram Recurrences and Central Functions of SL(2,C)-Character Varieties" , AMS Special Session on Geometry, Algebra, and Topology of Character Varieties, JMM, Jan 8, 2009. PDF Slides
• "Signed Graph Coloring, the Art of Linear Algebra, and a Theorem of Jacobi" (with Steve Morse), MathFest, July 31, 2008. PDF slides
• "The Character Variety's New Clothes" , AMS Session on Algebra and Number Theory, JMM 2008, Jan 7, 2008. PDF slides
• "The Art of Linear Algebra" , USMA Department of Mathematical Sciences Research Seminar, Dec 5, 2007. PDF slides and PDF handout
• "Trace Diagrams, Spin Networks, and Spaces of Graphs" , first of two invited lectures at the 7th KAIST Geometric Topology Fair in Gyeongju, Korea, July 10, 2007. PDF slides
• "Diagrammatic Central Functions" , second of two invited lectures at the 7th KAIST Geometric Topology Fair in Gyeongju, Korea, July 10, 2007. PDF slides
• "Trace Diagrams, Surfaces, and Character Varieties" , Kansas State University Mathematics Colloquium, April 15, 2007. PDF slides
• "Trace Diagrams, Surfaces, and Low-Dimensional Topology" , PhD Defense at the University of Maryland, Apr 25, 2006. PDF slides

Pursuit/Evasion and Cooperation

• "Subset Team Games, Cooperation Space, and Pursuit-Evasion Simulations" , 2009 ARL-USMA Technical Symposium, Nov 9, 2009.
• "Cooperation in a Network: Theoretical Considerations" (with Chris Arney), USMA Network Science Workshop, West Point, NY, Oct 29, 2009. PDF slides
• "The Mathematics of Pursuit and Evasion" , USMA Math Forum, March 26, 2009. PDF slides
• "Cooperation in Social Networks: Communication, Trust, and Selflessness" (with Chris Arney), Army Science Conference, Orlando, FL, Dec 2, 2008. PPTX Slides
• "Dynamic Mathematics and Pursuit-Evasion Games" , USMA Department of Mathematical Sciences Center for Faculty Development (Colloquium), Nov 20, 2008. PDF slides and PPTX slides and Applets Page
• "The Mathematics of Altruism and Selfish Cooperation" (with Chris Arney), ARL-USMA Technical Symposium, Atlantic City, NJ, Oct 23, 2008. PPTX slides
• "Altruism and Selfish Cooperation in Social Networks" (with Chris Arney and Lucas Gebhart), USMA Network Science Workshop, Oct 16, 2008. PPTX slides
• "Cooperating Teams in Pursuit-Evasion Games" , ARL-USMA Technical Symposium, Oct 30, 2007. PPT slides
• "Social Network Optimization and Synergy in Cooperative Systems: Trust & Selflessness" , USMA Network Science Workshop, Oct 23, 2007. PPT slides

Teaching and Technology

• "Using Data from Digital Imagery and Global Positioning Systems: Projects for Calculus" (with Frank Wattenberg), Applications Session, ICTCM, Mar. 13, 2010.
• "Java Applets for Pursuit and Evasion Games" , Military Applications Session, ICTCM, Mar. 13, 2010.
• "Multivariable Calculus Java Applets with Blaise" , MAA Session on Mathlets for Teaching and Learning Mathematics, JMM, Jan 16, 2010.
• "Java Mathlets with Blaise" , JMM session on Mathlets for Teaching and Learning Mathematics, JMM, Jan 7, 2009. PPTX Slides and PDF Slides and Applets Page
• "Dynamic Mathematics and Pursuit-Evasion Games" , USMA Department of Mathematical Sciences Center for Faculty Development (Colloquium), Nov 20, 2008. PDF slides and PPTX slides and Applets Page
• "Online Collaboration with a Wiki in Real Analysis" , session on Creative Uses of Emerging Technologies for Mathematics Teaching, MathFest 2008, Aug 1, 2008. PPT slides
• "Visualizing Lagrange Multipliers: a Discovery Approach to Constrained Optimization" , MAA session on Demos and Strategies with Technology that Enhance Teaching and Learning Mathematics, JMM 2008, Jan 7, 2008. PDF slides and demo page

Other