My research is in the area of operator algebras, typically of the separable nuclear variety. I have worked extensively on their structure and classification, and on exotic constructions with novel properties. Of particular note is my conjecture with Wilhelm Winter c. 2008 which asserts the equivalence of three regularity properties for simple separable nuclear C*-algebras: finite nuclear dimension, Z-stability, and strict comparison. It's almost a theorem by now. Let me know if you figure the last bit out. I've recently become very interested in Uniform Property Gamma, a new geometric threshold in nuclear C*-algebras. My papers can be found on the arXiv or MathSciNet.