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I work in computability theory, and am particularly interested in applying methods from computability theory to computable model theory, computable algebra, algorithmic randomness, and the computability theoretic and reverse mathematical analysis of combinatorial principles.
The articles in the Handbook of Recursive Mathematics (Ershov, Goncharov, Nerode, and Remmel, eds., Stud. Logic Found. Math. 138 - 139, Elsevier, Amsterdam, 1998) are a good introduction to computable model theory and related areas. See also Computability-Theoretic Complexity of Countable Structures by V. S.Harizanov.
My article Calibrating Randomness with R. Downey, A. Nies, and S. A. Terwijn is a survey of work in algorithmic randomness. A more recent and detailed survey is my book Algorithmic Randomness and Complexity with Downey.
My article Slicing the Truth is an introduction to the computability theoretic and reverse mathematical analysis of combinatorial principles.
My papers can be found on my website.