Sapere Aude Project

DSTOA Project



Papers and publications

Essentially all my papers can be found here on the arXiv.

Definability and almost disjoint families. Submitted.

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

Template iterations and maximal cofinitary groups. (With Vera Fischer). To appear in Fundamenta Mathematica.

The Sigma-1-2 counterparts to statements that are equivalent to the Continuum Hypothesis. (With William Weiss). To appear in the J. of Symbolic Logic.

Sigma-1-2 and Pi-1-1 mad families. In J. of Symbolic Logic

The isomorphism relation on separable C*-algebras is below a group action. (With G. Elliott, I. Farah, V. Paulsen, C. Rosendal and A. Toms). In Math. Res. Letters.

Set theory and von Neumann algebras. (With Martino Lupini). Appeared in Appalachian Set Theory (LMS Lecture notes 406, Cambridge University Press). pdf.

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

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

The conjugacy relation on unitary representations. (With G. Hjorth). 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.

Localized cohomology and some applications of Popa's cocycle superrigidity theorem. Israel J. Math. 181 (2011), 327-346.

A co-analytic maximal set of orthogonal measures. (with Vera Fischer). J. Symbolic Logic 75 (2010), no. 4, 1403-1414.

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

The effective theory of Borel equivalence relations. (With E. Fokina and S.D. Friedman). Ann. Pure Appl. Logic 161 (2010), no. 7, 837-850.

Definable Davies' theorem. (with William Weiss). Fund. Math. 205 (2009), no. 1, 77-89.

Borel reducibility and classification of von Neumann algebras. (with Roman Sasyk). Bull. Symbolic Logic 15 (2009), no. 2, 169-183.

Conjugacy, orbit equivalence and classification of measure-preserving group actions Ergodic Theory Dynam. Systems 29 (2009), no. 3, 1033-1049.

The classification problem for von Neumann factors. (with Roman Sasyk). J. Funct. Anal. 256 (2009), no. 8, 2710-2724.

Orbit equivalence and actions of $\Bbb F_n$. J. Symbolic Logic 71 (2006), no. 1, 265-282.