A (Very Brief) Introduction to My Work

I am a mathematician. This means that I am fluent in many things geometric and quantitative, and that I have an organized procedure for asking and investigating interesting questions. My research for the past few years has been focused on dynamical properties of rational functions using a number theory lens. Typically this involves discovering and explaining new phenomena about orbits of points under iteration of a function. I also think about questions related to arithmetic geometry, non-Archimedean geometry, and tropical geometry, and I am especially fond of algorithmic aspects of these subjects.

Recent Work

• Computing Automorphism Groups of Rational Functions
  with Michelle Manes and Bianca Viray. Submitted.
• Finite p-Irregular Subgroups of PGL₂(k). Submitted.
• Rational Functions with a Unique Critical Point. Submitted.
• Topology and Geometry of the Berkovich Ramification Locus for Rational Functions, II. Submitted.
• Prime Factors of Dynamical Sequences
  with Andrew Granville. To appear in Journal für die reine und angewandte Mathematik.
• On the Number of Places of Convergence of Newton's Method over Number Fields
  with José Felipe Voloch. Journal de Théorie des Nombres de Bordeaux. 23 (2011), 387-401.
• Metric Properties of the Tropical Abel-Jacobi Map
  with Matthew Baker. J. Algebraic Combin. 33 (2011), no. 3, 349-381.

Activities

• Seminar on Drinfeld Modules - University of Hawaii, Spring 2012
• Complex and Arithmetic Dynamics - ICERM Semester Program - Spring 2012
  I spoke in the workshop on Complex and p-adic Dynamics - February 13-17 - Lecture slides
  I co-organized the workshop on Global Arithmetic Dynamics - March 19-23
• Hawai'i Conference in Algebraic Number Theory, Arithmetic Geometry, and Modular Forms
  University of Hawaii, Honolulu, March 6-8, 2012
  I organized this workshop with the help of Pavel Guerzhoy, Zach Kent, Claude Levesque, and Michelle Manes. (Partially supported by NSF conference grant DMS-1162631)
• AMS Spring Western Section Meeting - University of Hawaii, Honolulu, March 3-4, 2012
  Special Session on Arithmetic Geometry (organized with Michelle Manes)