You can't understand anything without understanding where it came from. So as a phonologist, my main interests are in answering three related (sets of) questions:
How and why does sound change happen, and how does it relate to child language acquisition?
How much can models of diachrony explain synchronic facts, either about the phonologies of particular languages or about phonological typology?
What should a synchronic theory of phonology look like, once we've factored out the explanatory work that diachrony does for us?
I'm also interested in extending this way of thinking to other areas of the grammar, like morphology and syntax. I'm a historical linguist, really, but phonetics, speech perception, language acquisition, sociolinguistics, cultural evolution, and the mathematics of complex systems are all fields I'm trying to understand better.
My linguistic interests are in the history of the Indo-European languages and the reconstruction of Proto-Indo-European; so far I've worked on Greek, Latin, and Armenian.