Rafe Jones College of the Holy Cross Department of Mathematics and Computer Science Worcester, MA 01610 Office:  Swords 332 Phone:   (508) 793 - 2400 E-mail:  rjones [at] holycross [dot] edu

Courses:

Spring 2009

• Math 126: Calculus for Social Sciences 2 (TR 9:30-10:45)

• Math 244: Linear Algebra

Fall 2008

• Math 125: Calculus for Social Sciences 1, Section 4 (TR 9:30-10:45)

• Math 125: Calculus for Social Sciences 1, Section 5 (TR 8:00-9:15)

• Math 243: Algebraic Structures

Slides from past talks:

• "Prime Divisors in arithmetic dynamics" (AMS sectional at WPI, April 2009)
• "Critical orbits in arithmetic dynamics" (AMS sectional at U. of Illinois, March 2009)
• "Arboreal Galois representations" (Maine-Quebec number theory conference, September 2007)
• "Arboreal representations of abelian algebraic groups" (Number Theory Fest at U. of Illinois, May 2007)

Mathematical publications and preprints

• Rafe Jones and Han Peters.  "Blocks of monodromy groups in complex dynamics"  Submitted.   (Click here for preprint on the ArXiv.)

• Xander Faber, Benjamin Hutz, Patrick Ingram, Rafe Jones, Michelle Manes, Thomas J. Tucker, and Michael Zieve.  "On the geometry and arithmetic of pre-images for quadratic dynamical systems."   Math. Res. Lett.. 16 (1) (2009), 87-101.  (Click here for the preprint version on the ArXiv; PDF of 15 pages.)

• Rafe Jones and Jeremy Rouse.  "Iterated endomorphisms of abelian algebraic groups."  Submitted.   (Click here for preprint; PDF of 34 pages. You can also find this preprint on the ArXiv.)

• Nigel Boston and Rafe Jones.  "Settled polynomials over finite fields." (Click here for preprint; PDF of 13 pages.)

• Rafe Jones.  "Achievement sets of sequences."  Submitted. (Click here for preprint; PDF of 26 pages)

• Nigel Boston and Rafe Jones.  "The image of an arboreal Galois representation."   Pure and Applied Mathematics Quarterly 5 (1) (Special Issue: in honor of Jean-Pierre Serre, Part 2 of 2) (2009), 213-225.   (Click here for preprint; PDF of 13 pages)

• Rafe Jones. "The density of prime divisors in the arithmetic dynamics of quadratic polynomials."   J. Lond. Math. Soc. (2) 78 (2) (2008), 523--544.   (Click here for preprint version (some differences with published version); PDF of 23 pages. You can also find this preprint version on the ArXiv.)

• Rafe Jones. "Iterated Galois towers, associated martingales, and the p-adic Mandelbrot set." Compositio Math. 43 (5) (2007), 1108-1126.   (Click here for preprint version; PDF of 23 pages)

• Nigel Boston and Rafe Jones.  "Arboreal Galois representations." Geom. Dedicata. 124(1) (2007), 27-35 (electronic)   (Click here for preprint version; PDF of 12 pages)

• Rafe Jones. "Galois actions on rooted trees." Appears in Pro-p extensions of global fields and pro-p groups. Abstracts from the workshop held May 21-27, 2006. Organized by Nigel Boston, John Coates and Fritz Grunewald. Oberwolfach Rep. 3 (2006), no. 2, 1463-1535

• Rafe Jones and Jan Pearce. "A postmodern view of fractions and the reciprocals of Fermat primes." Math. Mag. 73 (2000), 83-97. Click here for preliminary version with figures omitted; PDF of 18 pages. Also click here to see our pictures of fractions on the cover of the issue where the article appeared.

Other publications and writing

• My dissertation is entitled "Galois Martingales and the Hyperbolic Subset of the p-adic Mandelbrot Set." You can see the introduction (PDF, 6 pages) or the whole thing (PDF, 90 pages of actual content). Note that to get the bibliography for the intro you'll have to look at the last three pages of the whole thing 

• "Ninety-One Years," [Poem] appeared in New Millenium Writings, June 2004. Click for the poem (PDF, 1 page)

• "In Code: A Mathematical Journey--A Book Review" appeared in the April 2003 issue of the Notices of the AMS .  Click here to go to the article (PDF, 2 pages)

• "Stern Perfection: Mathematics as a Fine Art," appeared in Brown University's Catalyst Special Edition , 2002. Click for the article (PDF, 3 pages)

• "A Summer at Discovery.com; appeared in the June/July 2002 issue of the Notices of the AMS .   Click here to go to the article (PDF, 3 pages)

Materials for my 2007-2008 job search:

• Survey article on Arboreal Galois representations
• CV
• Teaching Portfolio

2006 Wisconsin REU in Number Theory

Photo page

Miscellaneous stuff

For materials related to my 2005 job search, Click here