Nate's Research



Doc Brown -- one of my  previous lives.


book cover C*-algebras and finite-dimensional approximations can be purchased here. Taka and I will create an errata page someday. Maybe.


I post everything on the arXiv. (Though I'll gladly send you an older paper, if it isn't on the preprint server.)  

  1. (w/ Aaron Tikuisis and Aleksey Zelenberg) Rohklin dimension for C*-correspondences, 25 pages, preprint.
  2. (w/ Joan Bosa, Yasuhiko Sato, Aaron Tikuisis, Stuart White and Wilhelm Winter) Covering dimension of C*-algebras and 2-coloured classification, 87 pages, arXiv:1506.03974.
  3. (w/ Valerio Capraro) Groups associated to II_1 factors, Journal of Functional Analysis 264 (2013), 493-507.
  4. (w/ Erik Guentner) New C*-completions of discrete groups and related spaces, Bulletin of the London Mathematical Society 45 (2013), 1181-1193.
  5. Generalized inductive limits of quasidiagonal C*-algebras, Journal of Functional Analysis 262 (2012), 451--462.
  6. Topological dynamical systems associated to II_1 factors, Advances in Mathematics 227 (2011), 1665--1699.
  7. (w/ Wilhelm Winter) Quasitraces are traces: a short proof of the finite-nuclear-dimension case, Comptes Rendus Mathematiques de l'Academie des Sciences. La Societe Royal du Canada 33 (2011), 44--49.
  8. The symbiosis of C*- and W*-algebras, Contemporary Mathematics 534 (2011), 121--155. 
  9. (w/ Alin Ciuperca) Isomorphism of Hilbert modules over stably finite C*-algebras, Journal of Functional Analysis 257 (2009), 332--339. 
  10. (w/ Francesc Perera and Andrew Toms) The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras, Journal f{\"u}r die Reine und Angewandte Mathematik 621 (2008), 191--211.
  11. (w/ Ken Dykema and Kenley Jung) Free entropy dimension in amalgamated free products, Proceedings of the London Mathematical Society 97 (2008), 339--367.
  12. (w/ Andrew Toms) Three Applications of the Cuntz Semigroup, International Mathematics Research Notices 2007, no. 19, Art. ID rnm068, 14pp.
  13. Inductive limits, unique traces and tracial rank zeroBulletin of the London Mathematical Society 39 (2007), 377--383. 
  14. Quasidiagonality and the finite section method, Mathematics of Computation 76 (2007), 339--360.
  15. AF embeddings and the numerical computation of spectra in irrational rotation algebras,  Numerical Functional Analysis and Optimization 27 (2006), 517--528. 
  16. Invariant means and finite representation theory of C*-algebras, Memoirs of the  American Mathematical Society 184 (2006), no. 865, vi+105pp. 
  17. Kazhdan's Property T and C*-algebras, Journal of Functional Analysis 240 (2006), 290-296.
  18. Finite free entropy and free group factors, International Mathematics Research Notices 28 (2005), 1709-1715.
  19. Excision and a theorem of Popa, Journal of Operator Theory 54 (2005), 3-8. 
  20. (w/ Erik Guentner) Uniform embeddings of bounded geometry spaces into reflexive Banach space, Proceedings of the American Mathematical Society 133 (2005), 2045-2050.
  21. (w/ Ken Dykema) Popa algebras in free group factors, Journal f{\"u}r die Reine und Angewandte Mathematik 573 (2004), 157-180.
  22. Characterizing type I C*-algebras via entropy, Comptes Rendus Math{\'e}matique. Acad{\'e}mie des Sciences. Paris. 339 (2004), 827-829. 
  23. Connes' embedding problem and Lance's WEP, International Mathematics Research Notices 10 (2004), 501-510. 
  24. (w/ Marius Dadarlat) Extensions of quasidiagonal C*-algebras and K-theory,  Operator algebras and applications, 65--84, Advanced Studies in Pure Mathematics, 38, Mathematical Society of Japan, Tokyo,(2004). 
  25. On quasidiagonal C*-algebras, Operator algebras and applications, 19--64, Advanced Studies in Pure Mathematics, 38, Mathematical Society of Japan, Tokyo,(2004).
  26. (w/ Emmanuel Germain) Dual entropy in discrete groups with amenable actions.  Ergodic Theory and Dynamical Systems 22 (2002), 711-728. 
  27. (w/ Ken Dykema and Dima Shlyakhtenko) Topological entropy of free product automorphisms. Acta Mathematica 189 (2002), 1-35. 
  28. (w/ Marie Choda) Approximation entropies in crossed products with an application to free shifts. Pacific Journal of Mathematics 198 (2001), 331-346.
  29. Herrero's approximation problem for quasidiagonal operators. Journal of Functional Analysis 186 (2001), 360-365.
  30. Topological entropy, embeddings and unitaries in nuclear quasidiagonal C*-algebras.  Proceedings of the American Mathematical Society 128 (2000), 2603-2609. 
  31. Crossed products of UHF algebras by some amenable groups. Hokkaido Mathematics Journal 29 (2000), 201-211. 
  32. Topological entropy in exact C*-algebras. Mathematische Annalen 314 (1999), 347-367.
  33. AF-embeddability of crossed products of AF algebras by the integers. Journal of Functional Analysis 160 (1998), 150-175. 
  34. (w/ Nathan Dunfield and Greg Perry) Colorings of the plane III. Geombinatorics 3 (1994), 110-114.
  35. (w/ Nathan Dunfield and Greg Perry) Colorings of the plane II. Geombinatorics 3 (1994), 64-74. 
  36. (w/ Nathan Dunfield and Greg Perry) Colorings of the plane I. Geombinatorics 3 (1993), 24-31.