C* Algebras, Non-Commutative Differential Geometry.
My area of research is operator algebras and applications to geometry, with particular emphasis on commutative and non-commutative orbifolds and their C*-algebras. In particular, I established index theorems for orbifolds and orbifolds with boundary, investigated properties of orbifold elliptic operators, and characterized invariants of orbifold C*-algebras. Recently, my research has mainly focused on analysis on open orbifolds and orbifolds with boundary.
Orbifolds, which are generalized manifold groupoids, play an important role in many branches of mathematics and mathematical physics. Many symplectic quotients are for instance orbifolds, while in string theory, orbifolds describe regions "at infinity."
- K-Theoretical Index Theorems for Orbifolds, Quart. J. Math. 4 no. 170 (1992) 183-200.
- Abstract Characterization of Fixed Point Subalgebras of the Rotation Algebra, (with N, Watling). Canad. J. Math. 46 no. 6 (1994), 1211-1236.
- Soft Non-Commutative Toral C*-Algebras. J. Funct. Anal. 151 no. 1 (1997), 1-15.
- Soft C*-algebras. Proc. Edinburgh Math. Soc. (2) 45 no.1 (2002), 49-65.
- Orbifold Eta Invariants. Indiana Math. J. 56 no.2 (2007, 501-521.