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:



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