Research Interests

Free probability theory; von Neumann algebras; C*-algebras; L2-invariants; Poisson geometry.

Education

1991-1993 B.S., University of Nevada, Reno (high distinction)
1993-1997 Ph.D. University of California, Berkeley (thesis advisor: Prof. Dan-Virgil Voiculescu)

Former Graduate students

Dan Shiber (Ph.D. Sept 2008)
Jason Asher (Ph.D. June 2010)
Yoann Dabrowski (Ph.D. Dec 2010)
Benjamin Hayes (Ph.D. June 2014)
Paul Skoufranis (Ph.D. June 2014)
Brent Nelson (Ph.D. June 2015)
Ian Charlesworth (Ph.D. June 2017)

List of publications


  1. Free Quasi-Free States, C.R. Acad. Sci. Paris, t. 322, Serie I (1996), 645-649
  2. Free Quasi-Free States, Pacific J. Math, 177, (1997) 329-368
  3. Limit Distribution of Matrices with Bosonic and Fermionic Entries, Free Probability (D.-V. Voiculescu, ed.), Fields Institute Communications, vol. 12, AMS, 1997, pp. 241-25
  4. R-transform of Certain Joint Distributions, ibid, 253-256
  5. Gaussian Random Band Matrices and Freeness with Amalgamation, International Math. Res. Notices, 20 (1996), 1013-1025
  6. Some Applications of Freeness with Amalgamation, J. reine angew. Math. 500 (1998), 191-212
  7. A-valued Semicircular Systems, J. Funct. Anal., 166 (1999), 1\4
  8. Free Quasi-Free states, Thesis, UC Berkeley, 1997
  9. Gaussian random band matrices and operator-valued free probability theory, Proceedings of the Quantum Probability Conference, Banach Center Publ., 1998
  10. Free Entropy with Respect to a Completely-positive Map, American J. Math., 122 (2000), 45\81
  11. (with A. Nica and R. Speicher), Some minimization problems for the free analogue of Fisher information, Adv. Math., 121 (1999), 282--321
  12. (with A. Nica and R. Speicher), Maximality of the microstates free entropy for R-diagonal elements, Pacific J. Math., 187 (1999), 333--347\
  13. A Microstates Approach to Relative Free Entropy, Internat. J. Math. 13 (2002) 605--623\
  14. (with A. Nica and R. Speicher), R-diagonal elements and freeness with amalgamation, Canad. J. Math. 53 (2001) 355--381
  15. Survey paper: von Neumann algebras and Poisson manifolds, http://math.berkeley.edu/~aweinst/277papers/shlyakhtenko.tex
  16. Free Fisher information with respect to a completely positive map and cost of equivalence relations, Comm. Math. Phys. 218 (2001), 133--152
  17. (with K. Dykema), Exactness of Cuntz-Pimsner C*-algebras, Proc. Edinburgh Math. Soc. 44 (2001), 425-444
  18. Microstates Free Entropy and Cost of Equivalence Relations, Duke Math. J. 118 (2003), 375--425
  19. Prime type III factors, Proc. Nat. Acad. Sci., 97, 2000, 12439-12441
  20. (with Sorin Popa), Cartan subalgebras and bimodule decompositions of II1 factors, Math. Scand. 92 (2003) 93--102
  21. (with N. Brown and K. Dykema), Topological Entropy of Free Product Automorphisms, Acta Math. 189 (2002) 1--35
  22. (with Y. Ueda), Irreducible subfactors of L(F(infty)), J. Reine Angew. Math. 548  (2002) 149--166
  23. (with S. Popa), Universal properties of L(F(infty)) in subfactor theory, Acta Math. 191 (2003), no. 2, 225--257.
  24. (with A. Nica and R. Speicher), R cyclic families of matrices in free probability, J. Funct. Anal. 188 (2002) 227-271
  25. Free Fisher Information for Non-Tracial States, Pacific J. Math 211 (2003) 375--390
  26. (with G. Pisier) Grothendieck's Theorem for operator spaces, Invent. Math. 150 (2002) 185--217
  27. (with A. Nica and R. Speicher) Operator-valued distributions: I. Characterizations of freeness, Int. Math. Res. Notices 29 (2002) 1509-1438
  28. On the classification of Full Factors of Type III, Trans. AMS 356 (2004) 4143--4159
  29. On multiplicity and free absorption for free Araki-Woods factors, http://xxx.lanl.gov/abs/math.OA/0302217
  30. Some estimates for non-microstates free entropy dimension, with applications to q-semicircular families, Int. Math. Res. Notices 51 (2004) 2757--2772
  31. (with A. Connes) L2-homology for von Neumann algebras, J. Reine Angew. Math. 586 (2005), 125--168.
  32. (with I. Mineyev) Non-microstates free entropy dimension for groups,g Geom. Funct. Anal. 15 (2005), no. 2, 476--490.
  33. (with O. Radko) Picard groups of topologically stable Poisson structures, Pacific J. Math. 224 (2006), no. 1, 151--183
  34. (with K. Dykema and K. Jung) The Microstates Free Entropy Dimension of any DT-operator is 2, Doc. Math. 10 (2005), 247--261 (electronic)
  35. Remarks on free entropy dimension, Operator Algebras: The Abel Symposium 2004, 249--257, Abel Symp., 1, Springer, Berlin, 2006.
  36. Notes on free probability theory, http://xxx.lanl.gov/abs/math.OA/0504063
  37. A free analogue of Shannon's problem on monotonicity of entropy, Adv. Math. 208 (2007), no. 2, 824--833.
  38. (with K. Jung), Any generating set of an arbitrary property T von Neumann algebra has free entropy dimension $\le1$. J. Noncommut. Geom. 1 (2007), no. 2, 271--279.
  39. (with A. Guionnet), On classical analogues of free entropy dimension, J. Func. Anal. 251 No. 2 (2007), 738--771
  40. (with A. Guionnet), Free diffusions and matrix models with strictly convex interaction, Geom. Funct. Anal. 18 (2009), 1875-1916
  41. (with an appendix by H. Schultz), Shannon's monotonicity problem for free and classical entropy, Proc. Nat. Acad. Sci. 104 No. 39 15254-15258 (2007)
  42. Lower estimates on microstates free entropy dimension, Analysis & PDE, Vol. 2 (2009), No. 2, 119-146
  43. (with A. Guionnet and V.F.R. Jones), Random matrices, free probability, planar algebras and subfactors, in “Quanta of maths”, pp. 201–239, Clay Math. Proc., 11, Amer. Math. Soc., Providence, RI, 2010
  44. (with V.F.R. Jones and K. Walker), An orthogonal approach to the subfactor of a planar algebra, Pacific J. Math., Vol. 246 (2010), No. 1, 187-197
  45. (with S. T. Belinschi) Free probability of type B: analytic interpretation and applications, American Journal of Mathematics Vol. 134 (2012), 193-234.
  46. Free probability, Planar algebras, Subfactors and Random Matrices, Proceedings of the International Congress of Mathematicians (Hyderabad, India, 2010), Vol. III, Hindustan Book Agency, 2010, pp. 1603--1623
  47. (with C. Houdayer) Strongly solid II1 factors with an exotic MASA, International Mathematics Research Notices, Vol. 2011, No. 6, 1352–1380
  48. (with A. Guionnet and V.F.R. Jones), A semi-finite algebra associated to a planar algebra, J. Func. Anal., 261 (2011), 1345-1360
  49. On operator-valued free convolution powers, Indiana Univ. Math. J. 62 (2013), 91-97
  50. (with A. Guionnet; V.F.R. Jones and P. Zinn-Justin) Loop models, random matrices and planar algebras. Comm. Math. Phys. 316 (2012), no. 1, 45–97.
  51. On the Symmetric Enveloping Algebra of Planar Algebra Subfactors (with S. Curran and V.F.R. Jones), Trans. AMS 366 (2014) no. 1, 113–133
  52. (with A. Guionnet), Free Monotone Transport, Inv. Math. 197 (2014), 613-661
  53. (with P. Skoufranis), Freely independent random variables with non-atomic distributions, Trans. AMS 367 (2015), 6267-6291
  54. (with I. Charlesworth), Free entropy dimension and regularity of non-commutative polynomials. J. Funct. Anal. 271 (2016), no. 8, 2274–2292

Awards and honors

1993 University of Nevada, Reno Gold Medal
1994 US Department of Education National Needs fellowship
1994 NSF Graduate Research Fellowship
1996 Charles B. Morrey Award (UC Berkeley)
1998 NSF Postdoctoral Fellowship
1999 MSRI Postdoctoral Fellowship
2001 Sloan Foundation Fellowship
2002 Clay Mathematics Institute Special Project award
2004 R. Sorgenfrey Distinguished Teaching Award
2004 Bourbaki Seminar ”Free quasi-free states and factors of type III” by S. Vaes on my work.
2010 Invited talk, Int. Congress Mathematicians, Hyderabad, India
2012 Plenary talk, German Mathematical Society Annual Meeting

Editorial Boards

Transactions AMS (2007-10)
Memoirs AMS (2007-10)
Groups, Geometry and Dynamics

Positions Held

Hedrick Assistant Professor (1998-99), UCLA;
Assistant Professor (1999-01), Associate Professor (2001-03), Professor (2003-present), UCLA;
I served as the Graduate Vice-Chair in 2008-10, and as the Department Chair in 2012-15.