Education.

Dissertation advisor: Prof. D.-V. Voiculescu.

Awards and honors.

Member of the American Mathematical Society.

Research interests.

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. 241-252

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\47

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, to appear in Proceedings NCG

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, to appear in American J. Math.

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

Positions held.