Elisha Peterson's Publications and Talks

Paper/Talk Tags:

altruism blaise catpursuit cattech cattrace central-functions characteristic-equation character-varieties chris-arney combinatorics cooperation cooperative-systems determinants dodgson-condensation fair-division featured fixed-points game-theory geogebra in-progress invariant-theory invited java lagrange-multipliers linear-algebra lucas-gebhart mathematics-education mathlets multi-agent-systems online published pursuit-evasion recurrence recurrences social-networks sperners-lemma spin-networks steve-morse submitted synergy talk teaching technology thesis trace-diagrams trust unpublished utility-theory wikis with-student

Paper/Talk Pages by Date:

• 2009 (3)
  • July (2)
  • March (1)
• 2008 (31)
  • December (17)
  • September (14)

Scholarly Papers and Other Written Work

[arXiv search]

Published & Accepted for Publication

Trace Diagrams, Character Varieties, and Applications

• "Spin Networks and SL(2,C) Character Varieties" (with Sean Lawton), Handbook of Teichmuller Theory Volume II (Chapter 16), 2009, Athanae Papadopoulos, ed., EMS Publishing House. arXiv: math.QA/0511271
• "Trace Diagrams, Representations, and Low-Dimensional Topology" , PhD Thesis at the University of Maryland (advised by Bill Goldman), 2006. PDF

Pursuit/Evasion and Cooperation

• "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

Teaching and Technology

• "Using a Wiki to Enhance Cooperative Learning in a Real Analysis Course" , PRIMUS 19, pp. 18-28, 2009. journal link

Other

• "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
• "Combinatorial Proofs of a Generalized Sperner's Lemma" , undergraduate thesis at Harvey Mudd College (advised by Francis Su), 2000. PDF

Preprints

• "Trace Diagrams, Matrix Minors, and Determinant Identities" (with Steve Morse), submitted. arXiv:0903.1373
• "The Computation of SL(2,C) Central Functions" (with Sean Lawton), submitted. arXiv:0903.2372 (see also this mathematica notebook with combinatorial recurrence implementation)
• "On a Diagrammatic Proof of the Cayley-Hamilton Theorem" , submitted.
• "Cooperation in Subset Team Games: Altruism and Selfishness" , submitted.

Unpublished & Work 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.
• "Dynamic Cobwebbing with Geogebra" , online tutorial, 2008. link
• "A mathematical formalism for selfish and altruistic cooperation in social networks" (with Chris Arney), . PDF
• "A Not-so-Characteristic Equation: the Art of Linear Algebra" , unpublished expository article, 2008. arXiv:0712.2058

Talks since 2006

Trace Diagrams, Character Varieties, and Applications

• "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

• "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

• "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