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