My general area of interest is applied logic: the study of mathematical and conceptual tools for use in computer science, linguistics, artificial intelligence and other areas.

Applied logic is applied mathematics. It is logic looking outward, reaching towards the worlds in which logic is used and ultimately to the social world.

Here are a few of my current areas:

Coalgebra, and more generally: circularity in mathematics and computer science. Here I am especially interested in the relation of recursion and corecursion.

Modal logic, its generalizations and applications. My main project here concerns logics of epistemic actions, such as public announcements, cheating and lying in games, etc.

Foundations of the theory of recursion. Here I am trying to use coalgebra in connection with recursive program schemes.

Mathematics of language. There are a number of projects cooking: the axiomatization of C-command, some work on the program of model theoretic syntax, etc. Also, there is a textbook Mathematical Structure in Language in the works with Ed Keenan.

You can get a better idea of most of this by looking at some recent papers and also at the manifesto.