My pure mathematical research has centered around the Atiyah-Singer index theorem and its generalizations. (See here for a “bedside reading” introduction to the index theorem, writen by Nigel Higson and me for the Princeton Companion to Mathematics.) I have been particularly interested in index theorems whose value groups are derived from coarse geometry. C*-algebras and their K-theory provide the main technical tools.
Studying the index theorem led me to learn about the topology of high-dimensional manifolds, sometimes called “surgery theory”. My attempts to write an exposition of surgery theory are listed separately.
I was formerly on the editorial boards of a couple of journals, but I have resigned as in my present state I am unable to the job effectively. Let me encourage you, though, if you have an appropriate paper, to submit it to one of them: