Contact
Mail address
Microsoft Station Q
CNSI Bldg.
Office 2237
University of California
Santa Barbara, CA 931066105
Microsoft Station Q
CNSI Bldg.
Office 2237
University of California
Santa Barbara, CA 931066105
Email: zhenghwa@microsoft.com
Phone: (805) 8938828
Fax: (425) 7081426
Office: CNSI 2237
Administrative Assistant
Sean Fraer
seanfr@microsoft.com
Phone: (805) 8938828
Fax: (425) 7081426
Office: CNSI 2237
Administrative Assistant
Sean Fraer
seanfr@microsoft.com
Publications

Classification of closed topological 4manifolds with infinite cyclic fundamental group
UC San Diego Ph.D thesis, 1993

Mobius invariance of knot energy
(with S. Bryson, M. Freedman and Z.X. He)
Bull. AMS 28, 99 (1993).

Mobius energy of knots and unknots
(with with M. Freedman and Z.X. He)
Ann. of Math .139, 1 (1994).

CP2stable theory
(with M. Freedman)
Math. Res. Letters 1, 45 (1994).

On Bott polynomials
J. of Knot Theory and Its Ramifications 3, 537 (1994).

Classification of closed nonorientable 4manifolds with infinite cyclic fundamental group
Math. Res. Letters 2, 339 (1995).

Controlled linear algebra
(with M. Freedman)
Prospects in Topology; Proceedings of a conference in honor of William Browder, ed. Frank Quinn
Ann. of Math. Stud. 138, 138 (1995).

Integral geometry of plane curves and knot invariants
(with X.S. Lin)
J. Diff. Geom. 44, 74 (1996).

Burau representation of string links and random walks
(with X.S. Lin and Feng Tian)
Pac. J. of Math. 182, 289 (1998).

On Ohtsuki invariants of integral homology 3spheres
(with X.S. Lin)
Acta. Math. Sinica 15, 293 (1999).

Fermat limits, and a congruence of Ohtsuki's invariants
(with X.S. Lin)
Proceedings of the Kirbyfest, edited by J. Hass and M. Scharlemann
Geometry and Topology Monographs 2, 321 (1999).

Selfhomeomorphisms of 4manifolds with fundamental group Z
(with R. Stong)
Topology Appl. 106, 49 (2000).

The Gassner representation for string links
(with P. Kirk and C. Livingston)
Commun. Contemp. Math. 3, 87 (2001).

Random walks on knot diagrams, colored Jones polynomials, and IharaSelberg type zeta functions
(with X.S. Lin) Knots, braids, and mapping class groupspapers dedicated to Joan S. Birman (New York, 1998), 107121, AMS/IP, Stud. Adv. Math. 24 Providence, RI, (2001).

Simulation of topological field theories by quantum computers
(with M. Freedman and A. Kitaev)
Commun. Math. Phys. 227, 587 (2002).

A modular functor which is universal for quantum computation
(with M. Freedman and M. Larsen)
Commun. Math. Phys. 227, 605 (2002).

The twoeigenvalue problem and density of Jones representation of braid groups
(with M. Freedman and M. Larsen)
Comm. Math. Phys. 228, 177 (2002).

Quantum SU(2) faithfully detects mapping class groups modulo center
(with M. Freedman and K. Walker)
Geom. Topol. 6, 523 (2002).

Topological quantum computation
(with M. Freedman, A. Kitaev and M. Larsen) Mathematical challenges of the 21st century (Los Angeles, CA, 2000).
Bull. Amer. Math. Soc. (N.S.) 40, 31 (2003).

On Freedman's lattice model for topological phases
(with J. Brink)
Quantum Information Processing, 2, 81 (2003).

A class of P,T invariant topological phases of interacting electrons
(with M. Freedman, C. Nayak, K. Shentgel and K. Walker)
Annals of Physics, 310, 428 (2004).

Quantum logic as motivated by quantum computing
(with J. Dunn, T. Hagge and L. Moss),
Journal of Symbolic Logic, 70, iss. 2, 353 (2005).

Density of the SO(3) TQFT representation of mapping class groups
(with M. Larsen)
Comm. Math. Phys., 260, 641 (2005), math.GT/0408161

Universal manifold pairings and positivity
(with M. Freedman, A. Kitaev, C. Nayak, J. Slingerland, K. Walker)
Geometry and Topology, 9 53, 2303 (2005), math.GT/0503054

The Neigenvalue problem and two applications
(with M. Larsen and E. Rowell)
Math. Research Notices, 2005, iss. 64, 3987 (2005), math.RT/0506025

Extraspecial 2groups and the images of braid group representations
(with J. Franko, and E. Rowell)
J. of Knot Theory and Its Ramifications, 15, 1 (2006), math.RT/0503435

Topologization of electron liquids with ChernSimons theory and quantum computation
Nankai Tracts in Mathematics, 10, (2006), Editors Molin Ge and Weiping Zhang, World Scientific, pg. 106120, condmat/0601285.

Large quantum Fourier transforms are never exactly realized by braiding conformal blocks
(with M. Freedman)
Phys. Rev. A, 75, 032322 (2007).

Interacting anyons in topological quantum liquids: The golden chain
(with A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, M. Freedman)
Phys. Rev. Lett., 98, 160409 (2007); condmat/0612341

A classification of symmetric polynomials of infinite variables a construction of Abelian and non
Abelian quantum Hall states
(with X.G. Wen)
Phys. Rev. B, 77, 235108 (2008); condmat/0801.329

On (2+1)picture TQFTs
(with M. Freedman, C. Nayak, and K. Walker)
Topology and Physics  Proceedings of the Nankai Conference in Memory of XiaoSong Lin, Nankai Tracts in Mathematics, 12, 19 (2007) World Scientific Company (September 2008)

On exotic modular tensor categories
(with S. Hong, E. Rowell)
Commun. Contemp. Math. Supplementary Issue 1 (2008) pp. 10491074, math.GT/0710.5761

Topological properties of Abelian and nonAbelian quantum Hall states from the pattern of zeros
(with X.G. Wen)
Phys. Rev. B 78, 155109 (2008), arXiv:0803.1016

A short introduction to Fibonacci anyon models
(with S. Trebst, M. Troyer, A. Ludwig)
Prog. Theor. Phys. Suppl. 176, 384 (2008).

Emergence of nonabelian statistics from an abelian model
(with J. R. Wootton, V. Lahtinen, and J. K. Pachos)
Phys. Rev. B 78, 161102(R) (2008), arXiv:0804.0931

From string nets to nonabelions
(with L. Fidkowski, M. Freedman, C. Nayak, K. Walker)
Commun. Math. Phys. 287, 805827 (2009), condmat/0610583

On classification of modular tensor categories
(with E. Rowell, R. Stong)
Commun. Math. Phys. 292, 343389 (2009), math.QA/0712.1377

Topology driven quantum phase transitions in anyonic quantum liquids
(with C. Gils, S. Trebst, A. Kitaev, A. Ludwig, M. Troyer)
Nature Physics 5, 834 (2009), arXiv:0906.1579

Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
(with C. Gils, E. Ardonne, S. Trebst, A. Ludwig, M. Troyer)
Phys. Rev. Lett. 103, 070401 (2009).

Anyonic quantum walks
(with G. Brennen, D. Ellinas, V. Kendon, J. Pachos, I. Tsohantjis)
Annals of Physics 325, 664 (2010), arxiv:0910.2974

NonAbelian quantum Hall states and their quasiparticles: From the pattern of zeros to vertex algebra
(with Y. Lu, X.G. Wen, Z. Wang)
Phys. Rev. B 81, 115124 (2010), arxiv:0910.3988

Projective Ribbon Permutation Statistics: a Remnant of nonAbelian Braiding in Higher Dimensions
(with M. Freedman, M. B. Hastings, C. Nayak, X.L. Qi, K. Walker)
arXiv:1005.0583
Books
Topology and Physics
Proceedings of the Nankai International Conference in Memory of XiaoSong Lin
Tianjin, China 2731 July 2007 (Nankai Tracts in Mathematics)
Kevin Lin (Editor), Zhenghan Wang (Editor), Weiping Zhang (Editor)
World Scientific Publishing Company (September 2008)
Topological Quantum Computation
CBMS Regional Conference Series in Mathematics, vol. 112
American Mathematical Society (May 2010)