Publications

#### ‹Publication List›

1. Classification of closed topological 4-manifolds with infinite cyclic fundamental group ‹PDF›

2. Mobius invariance of knot energy ‹PDF›

3. Mobius energy of knots and unknots ‹PDF›

4. CP^{2}-stable theory ‹PDF›

5. On Bott polynomials ‹PDF›

6. Classification of closed nonorientable 4-manifolds with infinite cyclic fundamental group ‹PDF›

7. Controlled linear algebra ‹PDF›

8. Integral geometry of plane curves and knot invariants ‹PDF›

9. Burau representation of string links and random walks ‹PDF›

10. On Ohtsuki invariants of integral homology 3-spheres ‹PDF›

11. Fermat limits, and a congruence of Ohtsuki's invariants ‹PDF›

12. Self-homeomorphisms of 4-manifolds with fundamental group Z ‹PDF›

13. The Gassner representation for string links ‹PDF›

14. Random walks on knot diagrams, colored Jones polynomials, and Ihara-Selberg type zeta functions ‹PDF›

15. Simulation of topological field theories by quantum computers ‹PDF›

16. A modular functor which is universal for quantum computation ‹PDF›

17. The two-eigenvalue problem and density of Jones representation of braid groups ‹PDF›

18. Quantum SU(2) faithfully detects mapping class groups modulo center ‹PDF›

19. Topological quantum computation ‹PDF›

20. On Freedman's lattice model for topological phases ‹PDF›

21. A class of P,T invariant topological phases of interacting electrons ‹PDF›

22. Quantum logic as motivated by quantum computing ‹PDF›

23. Density of the SO(3) TQFT representation of mapping class groups ‹PDF›

24. Universal manifold pairings and positivity ‹PDF›

25. The N-eigenvalue problem and two applications ‹PDF›

26. Extraspecial 2-groups and the images of braid group representations ‹PDF›

27. Topologization of electron liquids with Chern-Simons theory and quantum computation ‹PDF›

28. Large quantum Fourier transforms are never exactly realized by braiding conformal blocks ‹PDF›

29. On (2+1)-picture TQFTs ‹PDF›

30. Interacting anyons in topological quantum liquids: the golden chain ‹PDF›

31. On exotic modular tensor categories ‹PDF›

32. A classification of symmetric polynomials of infinite variables-a construction of Abelian and non-Abelian quantum Hall states ‹PDF›

33. Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros ‹PDF›

34. Non-Abelian statistics from an Abelian model ‹PDF›

35. A short introduction to Fibonacci anyon models ‹PDF›

36. From string nets to nonabelions ‹PDF›

37. On classification of modular tensor categories ‹PDF›

38. Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids ‹PDF› ‹PDF›

39. Collective states of interacting anyons, edge States, and the nucleation of topological liquids ‹PDF›

40. Anyonic quantum walks ‹PDF›

41. Non-Abelian quantum Hall states and their quasiparticles: from the pattern of zeros to vertex algebra ‹PDF›

41-1. Knotting and quantum computing (in Chinese) ‹PDF›

42. Projective ribbon permutation statistics: a remnant of non-Abelian braiding in higher dimensions ‹PDF›

43. Quantum walks with non-abelian anyons ‹PDF›

44. A classification of 2D fermionic and bosonic topological orders ‹PDF›

45. Localization of unitary braid group representations ‹PDF›

46. Critical theory of the topological quantum phase transition in an S=2 chain ‹PDF›

47. (3+1)-TQFTs and topological insulators ‹PDF›

48. Galois conjugates of topological phases ‹PDF›

49. |Z_{Kup}|=|Z_{Henn}|^2 for Lens spaces ‹PDF›

50. Solutions to generalized Yang-Baxter equations via ribbon fusion categories ‹PDF›

51. Identifying topological order by entanglement entropy ‹PDF› ‹PDF›

51-1. Book review ‹PDF›

51-2. From FQHE to TQC (in Chinese) ‹PDF›

52. Quantum computing: a quantum group approach ‹PDF›

53. Pattern-of-zeros approach to fractional quantum Hall states and a classification of symmetric polynomial of infinite variables ‹PDF›

54. Metaplectic anyons, Majorana zero modes, and their computational power ‹PDF›

55. Anyonic quantum spin chains: Spin-1 generalizations and topological stability ‹PDF›

56. The third life of quantum logic: quantum logic inspired by quantum computing ‹PDF›

57. Test of Einstein-Podolsky-Rosen steering ‹PDF›

58. Lattice model for fermionic toric code ‹PDF›

59. Quantum fidelity, modular transformations, and topological orders in two dimensions

60. On arithmetic modular categories

61. Complexity classes as mathematical axioms II

62. On metaplectic modular categories and their applications ‹PDF›

63. On modular categories

64. Universal quantum computation with weakly integral anyons

65. Universal quantum computation with metaplectic anyons

66. Framed cord algebra invariants of knots in $S^1 \times S^2$

67. Symmetry, defects, and gauging of topological phases

68. On the classification of weakly integral modular categories

69. Local representations of the loop braid group

70. On enriching the Levin-Wen model with symmetry

#### Slides

1. Pattern of Zeroes ‹PDF›

2. Curve Diagrams ‹PDF›

3. Topological Phases of Matter ‹PDF›

4. Topological Quantum Computation ‹PDF›

5. Topological Phases of Matter ‹PDF›

#### ‹In Media›

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