Sapere Aude Project

DSTOA Project


DSTOA: Descriptive Set Theory and Operator Algebras

DSTOA was a research project under the EU's 7th framework programme, IRG-Marie Curie actions. It ran for 36 months from October 1, 2009 to September 30, 2012. The first 21 months of the project were carried out at the Kurt Goedel Research Center at the University of Vienna, Austria, and for the last 15 months the project was carried out at the Department of Mathematical Sciences, University of Copenhagen, Denmark. The principal researcher on the grant was Asger Tornquist.

The project focused on several problems, bound together by the fact that they all were problems that subject-wise were located at the boundary between descriptive set theory, operator algebras and ergodic theory.

The following papers are all directly or indirectly the outcome of the project. They me be viewed on the arXiv.

The Sigma-1-2 counterparts to statements that are equivalent to the Continuum Hypothesis. (With William Weiss). Preprint.

The Borel complexity of von Neumann equivalence. (With Inessa Epstein). Preprint.

Set theory and von Neumann algebras. (With Martino Lupini). To appear as a chapter in the book Appalachian Set Theory (Cambridge University Press). pdf.

The descriptive set theory of C$^*$-algebra invariants. (With I. Farah and A. S. Toms). To appear in Int. Math. Res. Notices.

Turbulence, orbit equivalence, and the classification of nuclear C*-algebras. (With I. Farah and A. S. Toms). To appear in J. fur die reine und angwandte Math.

The conjugacy relation on unitary representations. (With G. Hjorth). To appear in Math. Research Letters.

Projective maximal families of orthogonal measures with large continuum. (With V. Fischer and S.D. Friedman J. Logic and Analysis, vol. 4, 2012.

On the pointwise implementation of near-actions. Trans. Amer. Math. Soc. 363 (2011), no. 9, 4929-4944.

Turbulence and Araki-Woods factors. (with Roman Sasyk). J. Funct. Anal. 259 (2010), no. 9, 2238-2252.


In Vienna, the Scientist in Charge was Professor Sy-David Friedman, director of the Kurt Goedel Research Center. In Copenhagen the Scientist in Charge was Mikael Rordam.

In Vienna, Clinton Conley was employed in the project as a postdoc from the fall of 2010 to the spring of 2011.

The project also benefitted immensely from the assistance, practical and intellectual, of Jakob Kellner.