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My mathematical interests lie in C*-algebras and noncommutative geometry. More specifically, I am interested in Elliott's conjecture regarding K-theoretic classification of a certain class of C*-algebras. This program has seen great progress - beginning with Elliott's classification of noncommutative zero-dimensional spaces and followed by many others. However, the discovery of several counterexamples in recent years showed that the program's original scope had to be narrowed. It is speculated that the classifiable C*-algebras must be among those which are low dimensional in a sense which has not yet been made precise. The Toms-Winter conjecture is a promising contender for such a notion and it has been a subject of intense interest - with many cases already verified. I, too, am hoping to take part in this investigation.

Long overdue update (2/26/16): The rate at which research in this area has been going is astounding. As of August 2015, finite nuclear dimension has been shown to be enough for complete classification of what was conjectured to be the classifiable class of C*-algebras. Several significant results have followed from this classification: quasidiagonality of the conjectured classifiable class of C*-algebras (a result which has long resisted proof) and even a structure theorem about reduced group C*-algebras. It still remains to be seen if finite nuclear dimension can be relaxed to Z-stability, if the assumption of the UCT can be dropped, and if classification is possible without unitality.

My interests have shifted a bit since I last wrote. I am now looking to understand a conjectured systematic way of producing, for the irreducible unitary representations of any locally compact group, a parameter space after passage through K-functors.