I'm a Professor of Mathematics in the Department of Mathematics and Statistics here at Amherst College.

Previously, I was: a graduate student in the Math Department at Brown University, graduating in 1998;
then a Visiting Assistant Professor in the Math Department at the University of Rochester, from 1998 to 2000, and
then an NSF-sponsored Research Postdoc in the Math Department at Boston University, from 2000 to 2002.

The main focus of my research is arithmetic dynamics, which is the study of discrete dynamical systems in a number-theoretic context.
My particular interests include non-archimedean dynamics, arboreal Galois representations, and preperiodic points, preperiodic subvarieties, and points of small canonical height over global fields.

Courses

Math 121, Section 02 (Intermediate Calculus)    Fall 2024

Math 345 (Complex Analysis)    Fall 2024

Book

My book Dynamics in One Non-Archimedean Variable is a graduate-level textbook on the dynamics of rational functions defined over p-adic and other non-archimedean fields, published by the American Mathematical Society.

Errata list for this book. If you find other errors not listed here, please email me to let me know.

Solution to Exercise 8.16. This exercise in the book, to prove Theorem 8.15(f), is quite hard. See this link for a (nearly complete) solution.

Research

List of papers (includes abstracts and some pdf files)

Abbreviated Curriculum Vitae

Data from the Small Heights for Cubic Polynomials 2007 REU

Data from the Small Heights for Quadratic Polynomials 2011 REU

Data from the Small Heights for Quadratic Rational Functions 2011 REU

Slides from some of my talks

Five College Number Theory Seminar

Department of Mathematics and Statistics
Amherst College
P. O. Box 5000
Amherst, MA 01002-5000

Office: Seeley Mudd 406
Office Phone: (413) 542-8562
E-mail: rlbenedetto at amherst dot edu