Analysis is the study of estimates; Topology is the study of nearness; Combinatorics is the study of counting; Algebra is the study of tautologies.
You can jump to my list of papers or see my Google Scholar profile to get an idea of what I do.
My research interests are in commutative algebra, with leanings toward the homological. My current research is in the representation theory of local rings. In practice, this means thinking about relationships between the structure of a ring and the structure of the category of maximal Cohen-Macaulay modules over the ring. My work is funded by the National Security Agency and has been funded in the past by the National Science Foundation and the Clay Mathematics Institute.
Even more Executive Summary
Here’s a song about my research, and here’s a poem about pure mathematics in general.
Who else does those things?
The people listed at commalg.org/people, that’s who.