Rafe Jones College of the Holy Cross Department of Mathematics and Computer Science Worcester, MA 01610 Office:  Swords 332 Phone:   (608) 692 - 1627 E-mail:  rjones [at] holycross [dot] edu

• CV
• Survey article on Arboreal Galois representations

Mathematical publications and preprints

• Rafe Jones and Michelle Manes.  "Galois theory of quadratic rational functions." Submitted. (Click here for preprint on the ArXiv.)

• Rafe Jones.  "An iterative construction of irreducible polynomials reducible modulo all primes." Accepted for publication, J. Algebra. (Click here for preprint on the ArXiv.)

• Nigel Boston and Rafe Jones.  "Settled polynomials over finite fields." To appear, Proc. Amer. Math. Soc. (Click here for preprint; PDF of 15 pages.)

• Rafe Jones.  "Achievement sets of sequences."   Amer. Math. Monthly 118 (6) (2011), 508-521.  (Click here for preprint; PDF of 16 pages)

• Rafe Jones and Han Peters.  "Blocks of monodromy groups in complex dynamics."   Geom. Dedicata 150 (1) (2011), 137-150.  (Click here for preprint on the ArXiv.)

• Rafe Jones and Jeremy Rouse.  "Iterated endomorphisms of abelian algebraic groups."   Proc. Lond. Math. Soc. 100 (3) (2010), 763-794.  (Click here for preprint; PDF of 34 pages. You can also find this 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.)

• 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

• "Numbers: A Very Short Introduction--A Book Review"  appeared in the January 2012 issue of the Notices of the AMS.  Click here to go to the article (PDF, 2 pages)

• 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)

Slides from past talks:

• "Critical Orbits in Dynamics" (Wayne State Colloquium, November 2010)
• "Galois groups of rational functions with non-trivial automorphisms" (Maine-Quebec number theory conference, October 2009)
• "Galois actions on preimage trees" (Dynamical Numbers conference at Max Planck, July 2009)
• "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)

Courses:

Spring 2012

• Math 135: Calculus I

• Math 352: Modern Algebra II

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Fall 2011

• Math 135: Calculus I , sections 7 and 8

• Math 351: Modern Algebra I

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On leave Fall 2010 - Spring 2011

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Spring 2010

• Math 132: Calculus for Physical and Life Sciences II, section 4

• Math 352: Abstract Algebra II

Fall 2009

• Math 131: Calculus for Physical and Life Sciences I , sections 4 and 5

• Math 351: Abstract Algebra I

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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

2006 Wisconsin REU in Number Theory

Photo page

Miscellaneous stuff

For materials related to my 2005 job search, Click here