Computational Complexity
I am primarily interested in the NP problem (What is the power of nondeterminism?),
the BPP problem (What is the power of randomness?), and complexity in analysis
(especially geometric measure theory). I have developed three
analytic tools for investigating these problems:

Resourcebounded category (1987)

Resourcebounded measure (1991)

Resourcebounded dimension (2000)
These are complexitytheoretic generalizations of classical Baire category, Lebesgue measure, and Hausdorff dimension
(fractal dimension), respectively. Each provides a mathematical means of quantifying the sizes of
subsets of various complexity classes.
In recent years, many investigators have worked with these
tools, extending them and using them to shed new light on
a wide variety of topics in computational complexity.
I enjoy being a part of this ongoing effort.
Bibliographies
John Hitchcock maintains online bibliographies on resourcebounded
measure and effective
fractal dimensions, with links to available papers in the latter.