Research

I work in operator algebras, a subfield of analysis which originated in the study of  symmetries of quantum mechanical systems.   I am primarily interested in the von Neumann algebras and C*-algebras that arise from representations of groups and dynamical systems.

Articles

  • Noncommutative joinings III (with Jon Bannon, Kunal Mukherjee), Operators and Matrices, to appear.
  • Noncommutative joinings II (with Jon Bannon, Kunal Mukherjee), Groups, Geometry, and Dynamics, to appear.
  • Corrigendum to: A Galois correspondence for reduced crossed products of simple C*-algebras by discrete groups (with Roger Smith), Canadian Journal of Mathematics, published online May 2019.
  • A Galois correspondence for reduced crossed products of simple C*-algebras by discrete groups (with Roger Smith), Canadian Journal of Mathematics Volume 71, Issue 5 (2019), pp. 1103-1125
  • On Noncommutative joinings (with Jon Bannon, Kunal Mukherjee), International Mathematics Research Notices Volume 2018, Issue 15 (2018), Pages 4734–4779,.
  • Mixing and weakly mixing abelian subalgebras of type II_1 factors (with Junsheng Fang, Kunal Mukherjee), Journal of Functional Analysis, (2017) Volume 272, Issue 7, Pages 2697-2725.
  • Structural properties of close II_1 factors (with Erik Christensen, Allan Sinclair, Roger Smith, Stuart White, Alan Wiggins), Munster Journal of Mathematics 10 (2017), 19–37.
  • Intermediate subalgebras and bimodules for crossed products of general von Neumann algebras (with Roger Smith), International Journal of Mathematics, (2016) Volume 27, Issue 11.
  • The modular symmetry of Markov maps (with Jon Bannon, Kunal Mukherjee), Journal of Mathematical Analysis and Applications (2016), 439(2), pp. 701-708.
  • Bimodules in crossed products of von Neumann algebras (with Roger Smith), Advances in Mathematics (2015), 274(19), pp. 539-561.
  • Kadison-Kastler stable factors (with Erik Christensen, Allan Sinclair, Roger Smith, Stuart White, Alan Wiggins), Duke Mathematical Journal (2014),  163(14), pp. 2639-2686
  • A remark on the similarity and perturbation problems (with Erik Christensen, Allan Sinclair, Roger Smith, Stuart White, Alan Wiggins),  Comptes Rendus Mathematiques de l’Academie des Sciences. La Societe Royale du Canada. (2013) 35 (2). pp. 70-76
  • Bimodules over Cartan masas in von Neumann algebras, norming algebras, and Mercer’s theorem (with David Pitts, Vrej Zarikian), New York Journal of Mathematics (2013), 19, pp. 455-486.
  • Mixing subalgebras of finite von Neumann algebras (with Junsheng Fang, Kunal Mukherjee), New York Journal of Mathematics (2013), 19, pp. 343-366.
  • Type II_1 factors satisfying the spatial isomorphism conjecture (with Erik Christensen, Allan Sinclair, Roger Smith, Stuart White, Alan Wiggins), Proceedings of the National Academy of Sciences, U.S.A. (2012), 109(52), pp. 20338-20343.
  • Structure results for normalizers of II_1 factors,  International Journal of Mathematics (2011), 22(7), pp. 947-979
  • The radial masa in a free group factor is maximal injective (with Junsheng Fang, Mohan Ravichandran, Stuart White),  Journal of the London Mathematical Society (2010), 82(3), pp. 787-809.
  • Hochschild Cohomology of II_1 factors with Cartan masas, Proceedings of the Edinburgh Mathematical Society (2009), 52(02), pp. 287-295.