- My area of expertise is in a variety of aspects of Analysis. I am interested in Operator Algebras, in particular in the type of Algebras of Operators known as von Neumann algebras and C*-algebras. My work first emphasized the study of these objects via both functional analytic methods and methods from algebraic topology. More recently, I have conducted research on the relationship between harmonic analysis, wavelets and operator algebras. I am interested in wavelets and frames associated to fractal systems and the operators and operator algebras that arise from their study. I remain interested in C*-algebras that can be formed from discrete groups arising in wavelet theory; most recently I have studied twisted group C*-algebras corresponding to N-adic rational numbers, generalized wavelets that can be associated to higher rank graph algebras, and the relationship of these latter wavelets to the eigenspaces of certain Laplace-Beltrami operators.