Sapere AudeMy research is funded by a generous grant from the the Danish Council for Independent Research, as part of their elite career program known as "Sapere Aude" (level 2).
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 relative complexity of classification problems that arise in actual real life mathematics. Classification problems play a central role in essentially all areas of operator algebras, and in recent years the use of descriptive set theoretic techniques to study these classification problems has taken flight.
Some papers and preprints related to the project:
The project currently also funds a Ph.D. student (Karen Bakke Haga) and a postdoctoral fellow (David Schrittesser).