Department of Mathematics
Boulder, CO 80309
Office: Math 223
Email: thomas.gassert at colorado.edu
My primary field of research is Arithmetic Dynamics, which is the study of number theoretic properties of dynamical systems. In particular, I study number fields known as iterated extensions, which are named for their construction. Namely, if f is a monic polynomial with integer coefficients, and f n denotes the n-fold composition of f with itself, the iterated extensions are the number fields generated by the roots of f n. The roots of f n+1 are algebraic over the splitting field of f n, and thus the splitting fields of these polynomials are arranged in a tower. These iterated extensions are of interest for a variety of reasons; in my own work, I have used this construction to produce families monogenic fields of arbitrarily large degree.
I also have an interest in unit groups, and in particular, elliptic units. Following work of Greene and Hajir, I have written a program in GP-PARI which computes an "ideal" generating set of elliptic units in unrammified extensions of imaginary quadratic fields. The code is available here: [code]. (There are a few known bugs, so contact me before using.)