CURRICULUM VITAE

Ph.D., May 1998
Brown University, Mathematics
Dissertation: Fatou Components in p-adic dynamics
Advisor: Joseph Silverman

Sc.M., May 1996
Brown University, Mathematics

A.B., June 1993
Harvard University
Major: Mathematics
Magna Cum Laude, Phi Beta Kappa

[18] (with Dragos Ghioca, Pär Kurlberg, and Tom Tucker), The Dynamical Mordell-Lang Conjecture, submitted.
[17] (with Liang-Chung Hsia , A quotient of elliptic curves - weak Néron models for Lattès maps, in K.~Komatsu and K.~Hashimoto, eds., Proceedings of the 2007 Waseda Number Theory Symposium, Institute of Mathematics, Waseda University, 2007. (not peer-reviewed)
[16] (with Jean-Yves Briend and Hervé Perdry), Dynamique des polynômes quadratiques sur les corps locaux, Journal de Théorie des Nombres de Bordeaux, 19 (2007), 325-336.
[15] Heights and preperiodic points of polynomials over function fields, International Mathematics Research Notices, 2005, #62, 3855-3866.
[14] Preperiodic points of polynomials over global fields, Journal für die Reine und Angewandte Mathematik, 608 (2007), 123-153.
[13] An Ahlfors Islands Theorem for non-archimedean meromorphic functions, Transactions of the American Mathematical Society, accepted.
[12] Wandering domains in non-archimedean polynomial dynamics, Bulletin of the London Mathematical Society, 38 (2006), 937-950.
[11] Wandering domains and nontrivial reduction in non-archimedean dynamics, Illinois Journal of Mathematics 49 (2005), 167-193.
[10] (with John Benedetto ), A wavelet theory for local fields and related groups, The Journal of Geometric Analysis 14 (2004), 423-456.
[9] Examples of wavelets for local fields, in C. Heil, P. Jorgensen, D. Larson, eds., Wavelets, Frames, and Operator Theory, Contemporary Mathematics 345, AMS, Providence, 2004, pages 27-47.
[8] Non-archimedean holomorphic maps and the Ahlfors Islands Theorem, American Journal of Mathematics 125 (2003), 581-622.
[7] Examples of wandering domains in p-adic polynomial dynamics, Comptes Rendus Mathématique. Académie des Sciences. Paris, 335 (2002), 615-620.
[6] An elementary product identity in polynomial dynamics, The American Mathematical Monthly 108 (2001), 860-864.
[5] Components and periodic points in non-archimedean dynamics, Proceedings of the London Mathematical Society (3), 84 (2002), 231-256.
[4] Reduction, dynamics, and Julia sets of rational functions, Journal of Number Theory 86 (2001), 175-195.
[3] p-adic dynamics and Sullivan's No Wandering Domains theorem, Compositio Mathematica 122:3 (2000), 281-298.
[2] Hyperbolic maps in p-adic dynamics, Ergodic Theory and Dynamical Systems, 21 (2001), 1-11.
[1] (with William Goldman), The topology of the relative character varieties of a quadruply-punctured sphere, Experimental Mathematics 8:1 (1999), 85-103.

Amherst College, 2001-present, Assistant Professor.

Boston University, 2000-2002. NSF Mathematical Sciences Research Postdoc, to study p-adic and number-theoretic dynamics, under the mentorship of David Rohrlich and Bob Devaney.

University of Rochester, 1998-2000. Visiting Assistant Professor.

Brown University, 1993-1998. Graduate study.

University of Maryland, Summers of 1992, 1993. Undergraduate research under the supervision of William Goldman.

-- NSF Grant, Amherst College, 2006-2009.
-- Trustee Faculty Fellowship, Amherst College, 2005-2006.
-- NSA Young Investigator's Grant, Amherst College, 2004-2006.
-- Miner D. Crary Summer Research Fellowship, Amherst College, 2004.
-- NSF Mathematical Sciences Research Postdoc, 2000.
-- Nominated for Professor of the Year, University of Rochester, 2000.
-- Nominated for Professor of the Year, University of Rochester, 1999.
-- R.B. Lindsay Graduate Research Fellowship, Brown University, 1997-98.
-- Mathematics Department Outstanding Teaching Prize, Brown University, 1997.

-- Texas A&M Number Theory Seminar, Apr 24, 2007.
-- Texas A&M Undergraduate Mathematics Colloquium, Apr 24, 2007.
-- Special Session on Number Theory at the AMS Spring Eastern Sectional Meeting at Stevens Institute of Technology, Apr 14-15, 2007.
-- AMS Special Session on Arithmetic Geometry at the AMS-MAA Joint Meetings in New Orleans, Jan 8, 2007.
-- Amherst College Mathematics Colloquium, Oct 18, 2006.
-- Georgia Institute of Technology Algebra-Geometry-Topology Seminar, Apr 24, 2006.
-- University of Rochester Number Theory Seminar, Mar 1, 2006.
-- Colby College Mathematics Colloquium, Feb 20, 2006.
-- Williams College Mathematics Colloquium, Nov 18, 2005.
-- Five College Number Theory Seminar (Amherst, MA), Oct 25, 2005.
-- Maine/Québec Number Theory Conference, University of Maine, Orono, Oct 1-2, 2005.
-- IV Workshop in Dynamical Systems, Universidad Católica del Norte, San Pedro de Atacama, Chile, Aug 15-19, 2005.
-- University of Massachusetts TWIGS (The ``What Is ...?'' Graduate Seminar), Apr 7, 2005.
-- University of Connecticut Math Club Seminar, March 16, 2005.
-- AMS Special Session on Arithmetic Algebraic Geometry at the AMS-MAA Joint Meetings in Atlanta, Jan 7, 2005.
-- AMS-SIAM Special Session on Dynamic Equations on Time Scales, Integer Sequences and Rational Maps at the AMS-MAA Joint Meetings in Atlanta, Jan 6, 2005.
-- Wesleyan University Ergodic Theory and Dynamical Systems Seminar, Nov 9, 2004.
-- University of Connecticut Algebra Seminar, Oct 26, 2004.
-- Five College Number Theory Seminar (Amherst, MA), Oct 19, 2004.
-- Claremont Colleges Math Colloquium (at Pomona College), Oct 11, 2004.
-- MAA Northeastern Section Meeting at Roger Williams University, June 5, 2004.
-- Conference on Algebraic Dynamics, CUNY Graduate Center, May 29, 2004.
-- University of Wisconsin Number Theory Seminar, Mar 11, 2004.
-- AMS Special Session on Value Distribution Theory in Classical and p-adic Function Theory at the AMS-MAA Joint Meetings in Phoenix, Jan 10, 2004.
-- Brown University Algebra Seminar, Oct 27, 2003.
-- University of Waterloo Number Theory Seminar, Mar 4, 2003.
-- AMS Special Session on Wavelets, Frames and Operator Theory at the 2003 AMS-MAA Joint Meetings in Baltimore, Jan 18, 2003.
-- Five College Number Theory Seminar (Amherst, MA), Oct 29, 2002.
-- Five College Number Theory Seminar (Amherst, MA), Apr 30, 2002.
-- Short Course on p-adic Dynamics, Växjö University, Mar 19--21, 2002.
-- Ohio State University Number Theory Seminar, Feb 5, 2002.