On March 7 I am giving the Applied Algebra seminar at Berkeley.
On April 1 I am giving the Galois seminar at Penn.
I will be speaking at the Sixth Annual Upstate NY Number Theory Conference, April 30-May 1.
From May 16-20 I will be attending the workshop on The Galois Theory of Orbits in Arithmetic Dynamics at AIM in San Jose, CA.
In Fall 2016 I will be joining the math department at Texas A&M as an Instructional Assistant Professor.
My research interests are primarily in number theory and algebraic geometry, and more specifically in arithmetic dynamics. I study algebraic, arithmetic, and combinatorial properties of dynamical systems, such as ramification of primes in fields generated by preimages of a given point under a rational map, or how the number of periodic points of a map changes as the underlying field varies. I am also very interested in the applications of finite automata to algebra and number theory.
Courses Offered (subject to change)
- MTH 161 Calculus IA
- MTH 236 Introduction to Algebra I
- “Automatic Sequences and Curves over Finite Fields,“ in preparation.
- “ABC Implies a Zsigmondy Theorem for Ramification in Preimage Fields,“ with Thomas J. Tucker, in preparation.
- “Finite Ramification for Preimage Fields of Postcritically Finite Morphisms,” with Patrick Ingram, Rafe Jones, Jamie Juul, Alon Levy, Michelle Manes, Simon Rubinstein-Salzedo, and Joseph H. Silverman, submitted.
- “The Artin-Mazur Zeta Function of a Dynamically Affine Rational Map in Positive Characteristic,” J. Théor. Nombres Bordeaux, to appear.
- “On the Number of Distinct Functional Graphs of Affine-Linear Transformations over Finite Fields,” with Eric Bach, Linear Algebra and Appl. 439 (2013), pp. 1312-1320.
- “Transcendence of The Artin-Mazur Zeta Function for Polynomial Maps of 𝔸1(𝔽p)”Acta Arith. 156 (2012) no. 3, 293-300
- “A Count of Maximal Small Copies in Multibrot Sets,” with Rodrigo Pérez, Nonlinearity Vol. 18 No. 5, 2005.