716 Van Vleck Hall
University of Wisconsin-Madison
This semester I am a research assistant for Eric Bach. I will be graduating this July and starting in the Fall 2014 semester as a Visiting Assistant Professor at the University of Rochester.
My research interests are primarily in number theory, computational algebra, and algebraic geometry. Currently I am studying arithmetic dynamics, in particular the dynamics of polynomials and rational functions over finite fields. I am also very interested in the applications of finite automata to algebra and number theory. My advisor is Eric Bach. Here is my CV.
"State Complexity of Power Series and Cartier Orbits on Curves," in preparation.
"The Artin-Mazur Zeta Function of a Dynamically Affine Rational Map in Positive Characteristic," submitted.
"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 A^1(F_p)," 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.
Here is a video of a talk I gave at the May 2013 BIRS workshop on "The Art of Iterating Rational Functions over Finite Fields" that summarizes some of my research. You can also view the slides from the talk.