Nate's Research

 

    

Doc Brown -- one of my  previous lives.
 

I study operator algebras.  Why?  Well, partly due to their fundamental importance and yadda yadda yadda, but mostly `cause I like it and it pays the bills.  (I considered professional hockey, but I can't skate; thought about sumo wrestling, though I haven't the weight; televangelism sounds nice...and the pay is apparently great!!) 

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

Papers  

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

  1. (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 (to appear).
  2. (w/ Ken Dykema and Kenley Jung) Free entropy dimension in amalgamated free products, Proceedings of the London Mathematical Society (to appear).
  3. (w/ Andrew Toms) Three Applications of the Cuntz Semigroup, International Mathematics Research Notices 2007, no. 19, Art. ID rnm068, 14pp.
  4. Inductive limits, unique traces and tracial rank zero, Bulletin of the London Mathematical Society 39 (2007), 377--383. 
  5. Quasidiagonality and the finite section method, Mathematics of Computation 76 (2007), 339--360.
  6. AF embeddings and the numerical computation of spectra in irrational rotation algebras,  Numerical Functional Analysis and Optimization 27 (2006), 517--528. 
  7. Invariant means and finite representation theory of C*-algebras, Memoirs of the  American Mathematical Society 184 (2006), no. 865, vi+105pp. 
  8. Kazhdan's Property T and C*-algebras, Journal of Functional Analysis 240 (2006), 290-296.
  9. Finite free entropy and free group factors, International Mathematics Research Notices 28 (2005), 1709-1715.
  10. Excision and a theorem of Popa, Journal of Operator Theory 54 (2005), 3-8. 
  11. (w/ Erik Guentner) Uniform embeddings of bounded geometry spaces into reflexive Banach space, Proceedings of the American Mathematical Society 133 (2005), 2045-2050.
  12. (w/ Ken Dykema) Popa algebras in free group factors, Journal f{\"u}r die Reine und Angewandte Mathematik 573 (2004), 157-180.
  13. Characterizing type I C*-algebras via entropy, Comptes Rendus Math{\'e}matique. Acad{\'e}mie des Sciences. Paris. 339 (2004), 827-829. 
  14. Connes' embedding problem and Lance's WEP, International Mathematics Research Notices 10 (2004), 501-510. 
  15. (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). 
  16. On quasidiagonal C*-algebras, Operator algebras and applications, 19--64, Advanced Studies in Pure Mathematics, 38, Mathematical Society of Japan, Tokyo,(2004).
  17. (w/ Emmanuel Germain) Dual entropy in discrete groups with amenable actions.  Ergodic Theory and Dynamical Systems 22 (2002), 711-728. 
  18. (w/ Ken Dykema and Dima Shlyakhtenko) Topological entropy of free product automorphisms. Acta Mathematica 189 (2002), 1-35. 
  19. (w/ Marie Choda) Approximation entropies in crossed products with an application to free shifts. Pacific Journal of Mathematics 198 (2001), 331-346.
  20. Herrero's approximation problem for quasidiagonal operators. Journal of Functional Analysis 186 (2001), 360-365.
  21. Topological entropy, embeddings and unitaries in nuclear quasidiagonal C*-algebras.  Proceedings of the American Mathematical Society 128 (2000), 2603-2609. 
  22. Crossed products of UHF algebras by some amenable groups. Hokkaido Mathematics Journal 29 (2000), 201-211. 
  23. Topological entropy in exact C*-algebras. Mathematische Annalen 314 (1999), 347-367.
  24. AF-embeddability of crossed products of AF algebras by the integers. Journal of Functional Analysis 160 (1998), 150-175. 
  25. (w/ Nathan Dunfield and Greg Perry) Colorings of the plane III. Geombinatorics 3 (1994), 110-114.
  26. (w/ Nathan Dunfield and Greg Perry) Colorings of the plane II. Geombinatorics 3 (1994), 64-74. 
  27. (w/ Nathan Dunfield and Greg Perry) Colorings of the plane I. Geombinatorics 3 (1993), 24-31.
     

Here is a link to my CV.  Fellowships and grants can be found here. Any idea how many children died of malnutrition related diseases in the last 24 hours?  About 16,000! And 16,000 more will be dead before tomorrow. And the day after that, and the day after that. If you have time on your hands, here's a thought: save a child's life! It will be the most important thing you ever do.