R. Jason Parsley

Main Research interest: Topology & Geometry

Ideas combining low-dimensional topology & geometry, often with a bit of physics thrown in. Some examples:

• helicity of 3-dim. (and 2n+1-dim.) vector fields
• writhe of knots & other geometric/physical knot theory concerns
• ropelength of knots & its applications
• symmetries of knots & links

Voting Theory

In my spare time, I think about voting theory.

• the geometry (polytopes) & combinatorics (posets) of weighted voting
• a (possibly) new power index
• applications of topology to ranking
• exit polls: my first-year seminar conducted (successfully!!!) an exit poll for Forsyth County in the 2008 election

Window on Wake Forest: my discussion of math and voting, Nov. 2008

My two advisors and me, April 2004
Herman Gluck, me, and Dennis DeTurck

Publications

1. "Understanding geometry in the dance studio", Jason Parsley and Christina Soriano,
   J. of Mathematics and the Arts, 3:1, March 2009, 11-19, doi:10.1080/17513470902864262


2. "A new cohomological formula for helicity in R^{2k+1} reveals the effect of a diffeomorphism on helicity", Jason Cantarella and Jason Parsley,
   J. of Geometry & Physics, 60:9, Sept. 2010, 1127-1155, DOI: 10.1016/j.geomphys.2010.04.001.
   arxiv:0903.1465


3. "An infinite family of convex Brunnian links in R^n", Bob Davis, Hugh Howards, Jonathan Newman, and Jason Parsley,
   Geometriae Dedicata, 155:1, 141-149, Dec. 2011
   arxiv:1101.4863


4. "The Biot-Savart operator and electrodynamics on subdomains of the three-sphere",
   J. Math. Phys., to appear, Jan. 2012 (tentative date)
   arxiv:0904.3524



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5. "Intrinsic symmetry groups of links with 8 and fewer crossings", Michael Berglund, Jason Cantarella, Meredith Perrie Casey, Ellie Dannenberg, Whitney George, Aja Johnson, Amelia Kelly, Al LaPointe, Matt Mastin, Jason Parsley, Jacob Rooney, Rachel Whitaker,
   submitted. arxiv:1010.3234


6. "A student-run exit poll successfully predicts 2008 election results",
   Annalaissa Johnson, Andrew McCarty, Jason Parsley, and Robert Reinhard, submitted


7. "A geometric and combinatorial view of weighted voting",
   Sarah Mason and Jason Parsley
   submitted. arxiv:1109.1082



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8. "Existence and computation of Taylor states"
   Jason Parsley, in preparation


9. "The 27 possible intrinsic symmetry groups of 2-component links"
   Jason Cantarella, James Cornish, Matt Mastin, and Jason Parsley, in preparation


10. A geometric power index for weighted voting''
    Annalaissa Johnson, Sarah Mason, and Jason Parsley, in preparation


11. "Power indices for 5 voters''
    Annalaissa Johnson and Jason Parsley, in preparation

Dissertation: The Biot-Savart operator and electrodynamics on the three-sphere (pdf)

Master's Thesis: The Taylor problem in plasma physics (pdf)

CV