When I was in the program (1986-1990), the broad question I most
wanted to get an answer to was how to obtain greater generalizations
towards language universals. In my dissertation, I addressed the
question of why contour tones could split into level tones in some
languages but not in others. A popular proposal at the time, following
the principles-and-parameters approach of Chomsky (1981), attributed
the difference to a parameter, so that some contour tones split and
some do not. But the parameter seemed to restate the problem, rather
than explaining it. A better solution emerged when I noticed a
correlation between the stability of contour tones and the weight of
syllables: contour tones tend to split in languages whose syllables
are mostly CV and not in languages whose syllables are mostly CVX. The
connection between syllable structure and tone split can be made
though metrical theory, in particular the Weight-Stress Principle and
the determination of tonal domains as stress domains (through word and
phrasal stress).
My experience made me wary of parameter-based solutions, which are
still common, including their reincarnation in Optimality Theory as
factorial typology. In addition, it made me aware of the shortcoming
of looking at a problem in isolation, and the importance of
considering the interactions among related fields. For example, in my
recent work, I have argued that, if we try to account for all
phonotactic patterns by phonology alone, then the maximal syllable can
look rather large and complicated. However, if we consider both
morphological and phonological factors, then the maximal syllable in
many languages is smaller than it appears. The search for language
universals remains difficult, but I am optimistic that there is a lot
to gain.