The project, entitled "The complexity of classification problems arising in operator algebras", focuses on classification problems in the areas of C*-algebras and von Neumann algebras, but from the novel perspective of Descriptive Set Theory. The descriptive set theory of "definable" (Borel, analytic, etc.) equivalence relations provides a natural setting in which one can study the
- The descriptive set theory of C*-algebra invariants. (Joint with I. Farah and A. Toms, IMRN)
- The Borel complexity of von Neumann equivalence. (Joint with I. Epstein.)
- Turbulence, orbit equivalence, and the classification of nuclear C*-algebras (with I. Farah and A. Toms., J. fur die reine und angewandte Math.)
The project currently also funds a Ph.D. student (Karen Bakke Haga) and a postdoctoral fellow (David Schrittesser). |