Department of Mathematics
Box 395
Boulder, CO 80309
Office: Math 223
Email: thomas.gassert at colorado.edu

Research

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.)

CV

Preprints:
1. A note on the monogeneity of power maps. Preprint.
2. Discriminants of simplest 3n-tic extensions. Functiones et Approximatio Commentarii Mathematici (to appear). Preprint.
3. Discriminants of Chebyshev radical extensions. Journal de Théorie Nombres de Bordeaux, 26(3):607--633, 2014. Preprint.
4. Chebyshev action on finite fields. Disc. Math., 315--316:83--94, 2014. Preprint.