I work in operator algebras and applications and connections with K-theory, dynamical systems, statistical mechanics and conformal quantum field theory.
I published with Yasuyuki Kawahigashi a monograph Quantum Symmetries on Operator Algebras – the combinatorial and physical aspects of operator algebras (see here for the list of updates/corrections). This is a continuation of my previous collaborations with Huzihiro Araki and John Lewis on a C*-algebra approach to phase transitions in the two-dimensional Ising model.
I have also had interests in the study of amenable C*-algebras by K- theoretic or topological invariants, e.g. the expression of finite amenable simple C*- algebras as the inductive limit of simpler building blocks – George Elliott and I expressed the irrational rotation algebras as inductive limits of circle algebras. There is much interchange of ideas from amenable subfactors and amenable C*-algebras in this work (e.g. through common ideas from orbifolds and Rokhlin properties of automorphisms).
Recent work has focused on the study of modular invariant partition functions through subfactors and twisted equivariant K-theory – the latter being a programme of research with Terry Gannon.
David E Evans 