Publications

  • Journal Papers

1. Asymptotics of Nahm sums at roots of unity, (with D. Zagier), Ramanujan J. in press.

2. A meromorphic extension of the 3D Index, (with R. Kashaev), Research in Mathematical Sciences, Research in Mathematical Sciences, 6 (2019) no. 1, 6:8.

3. Quantum modularity and complex Chern-Simons theory, (with T. Dimofte), Commun. Number Theory Phys., 12 (2018) 1–52.

4. The colored HOMFLY-PT polynomial is q-holonomic, (with A. Lauda and T.T.Q. Le), Duke Math. J., 167 (2018) 397–447.

5. Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds, (with A. Reid), J. of Topology and Analysis, 10 (2018) 1–25.

6. A survey of q-holonomic functions, (with T.T.Q. Le), L’ Enseignement Mathematique, 62 (2) (2016) 501–525.

7. Quadratic integer programming and the slope conjecture, (with R. van der Veen), New York J. Math. 22 (2016) 907–932.

8. The 3D-index and normal surfaces, (with C. Hodgson, N. Hoffman and H. Rubinstein), Illinois J. of Mathematics, 60 (2016) 289–353.

9. Knots, BPS states, and algebraic curves, (with P. Kucharski, and P. Sułkowski), Commun. Math Physics, 346 (2016) 75–113.

10. The 3D-index of an ideal triangulation and angle structures, Ramanujan J. 40 (2016), 573–604.

11. A stability conjecture for the colored Jones polynomial, (with T. Vuong), Topology Proc. 49 (2017), 211–249.

12. A census of tetrahedral hyperbolic manifolds, (with E. Fominykh, M. Goerner, V. Tarkaev and A. Vesnin), Experimental Math. 25 (2016) 466–481.

13. Exact computation of the n-loop invariants of knots, (With E. Sabo and S. Scott), Experimental Math. 25 (2016) 125–129.

14. Evaluation of state integrals at rational points, (with R. Kashaev), Commun. Number Theory Phys. 9 (2015) no. 3, 549–582.

15. Flag algebras and the stable coefficients of the Jones polynomial, (with S. Norin and T. Vuong), European J. Combinatorics, 51 (2016) 165–189.

16. The symplectic properties of the PGL(n, C)-gluing equations, (with C. Zickert), Quantum Topol., 7 (2016), no. 3, 505–551.

17. 1-efficient triangulations and the index of a cusped hyperbolic 3-manifold, (with C. Hodgson, H. Rubinstein and H. Segerman), Geometry and Topology, 19 (2015) 2619–2689.

18. Gluing equations for PGL(n, C)-representations of 3-manifolds (with M. Goerner and C. Zickert), Alg. Geom. Topology, 15 (2015) 565–622.

19. Links with trivial Alexander module and nontrivial Milnor invariants, Chelyabinsk Math Journal, 3 (358) (2015) 41–49.

20. Algebraic G-functions of matrices over a group-ring, (with J. Bellissard), Chelyabinsk Math Journal, 3 (358) (2015) 50–61.

21. The complex volume of SL(n, C) representations of 3-manifolds (with D.P. Thurston and C. Zickert), Duke Math. J., 164 (2015) 2099–2160.

22. Recurrent sequences of polynomials in 3-dimensional topology, Acta Math. Vietnamica, 39 (2014) 541–548.

23. The Ptolemy field of 3-manifold-representations, (with M. Goerner and C.Zickert), Alg. Geom. Topology, 15 (2015) 371–397.

24. Nahm sums, stability and the colored Jones polynomial, (with T.T.Q. Le), Research in Mathematical Sciences, 2 (2015) 55 pp.

25. A generating series for Murakami-Ohtsuki-Yamada graph evaluations, (with R. van der Veen), Acta Math. Vietnamica, 39 (2014) 529–539.

26. From state integrals to q-series, (with R. Kashaev), Math. Research Letters, 24 3 (2017) 781–801.

27. Alternating knots, planar graphs and q-series, (with T. Vuong), Ramanujan J., 36 (2015) 501–527.

28. Irreducibility of q-difference operators and the knot 74 (with C. Koutschan), Alg. Geom. Topology, 13 (2013) 3261–3286.

29. Rationality of the SL(2, C)-torsion in dimension three (with J. Dubois), Topology Proceedings, 47 (2016) 115–134.

30. The quantum content of the gluing equations, (with T. Dimofte), Geometry and Topology, 17 (2013) 1253–1315.

31. Asymptotics of classical spin networks, (with R. van der Veen), Geometry and Topology, 17 (2013) 1–37.

32. Analyticity of the planar limit of a matrix model, (with I. Popescu), Annales Henri Poincare,´ 14 (2013) 499–565.

33. Quantum Knot Invariants, Mathematische Arbeitstagung (2011), Research in the Mathematical Sciences, 5 (2018) 5:11.

34. Twisting q-holonomic sequences by complex roots of unity, (with C. Koutschan), ISSAC 2012 Proceedings of 37th International Symposium on Symbolic and Algebraic Computation, (2012) 179–186.

35. The non-commutative A-polynomial of the (−2, 3, n) pretzel knots, (with C. Koutschan), Experimental Math, 21 (2012) 241–251.

36. The SL3 colored Jones polynomial of the trefoil (with H. Morton and T. Vuong), Proceedings of the AMS, 141 (2013) 2209–2220.

37. Asymptotics of the colored Jones function of a knot, (with T.T.Q. Le), Geometry and ˆ Topology, 15 (2011) 2135–2180.

38. Incompressibility criteria for spun-normal surfaces, (with N. Dunfield), Transactions of the AMS, 364 (2012) 6109–6137.

39. The A-polynomial of the (−2, 3, n) pretzel knots, (with T. Mattman), New York J. Math. 17 (2011) 269–279.

40. The SL3 Jones polynomial of the trefoil: a case study of q-holonomic sequences, (with C. Koutschan), Advances in Applied Math. 47 (2011) 829–839.

41. The degree of a q-holonomic sequence is a quadratic quasi-polynomial, Electronic J. Combinatorics, 18 (2011) research article P4, 23 pages.

42. Asymptotics of the instantons of Painlev´e I(with A. Its, A. Kapaev and M. Marino), Int. Math. Res. Not. IMRN 3 (2012) 561-–606.

43. Asymptotics of quantum spin networks at a fixed root of unity, (with R. van der Veen), Math. Annalen, 352 (2012) 987–1012.

44. What is a sequence of Nilsson type?, Contemporary Mathematics, 541 (2011) 145–157.

45. Knots and tropical curves, Contemporary Mathematics, 541 (2011) 83–111.

46. The Jones slopes of a knot, Quantum Topol., 2 (2011) 43–69.

47. Sum-integral interpolators and the Euler-Maclaurin formula for polytopes, (with J. Pommersheim), Transactions of the AMS 364 (2012) 2933–2958.

48. Behavior of knot invariants under genus 2 mutation (with N. Dunfield, S. G., A. Shumakovitch and M. Thislethwaite), New York J. Mathematics 16 (2010) 99–123.

49. An algorithm for the recursion of hypergeometric multisums(with X. Sun), Contemporary Mathematics, AMS 517 (2010) 143–156.

50. Universality and asymptotics of graph counting problems in nonorientable surfaces, (with M. Marino) J. Combin. Theory A ˜ 117 (2010) 715–740.

51. The non-commutative A-polynomial of twist knots(with X. Sun), Journal of Knot Theory and its Ramifications, 19 (2010) 1571–1595.

52. Analytiticy of the free energy of a closed 3-manifold (with T.T.Q. Le and M. Mari ˆ no) ˜ SIGMA, 4 (2008) 080, 20 pages.

53. G-functions and multisum versus holonomic sequences, Advances in Mathematics 220 (2009) 1945–1955.

54. Chern-Simons theory, analytic continuation and arithmetic, Acta Math. Vietnamica, 33 (2008) 335–362.

55. Resurgence of the fractional polylogarithms, (with O. Costin), Mathematical Research Letters 16 (2009) 817–826.

56. Resurgence of the Kontsevich-Zagier series, (with O. Costin), Annales de l’ Institut Fourier, 61 (2011) 1225–1258.

57. An ansatz for the asymptotics of hypergeometric multisums, Advances in Applied Mathematics, 41 (2008) 423–451.

58. An extended version of additive K-theory, Journal of K-theory 4 (2009) 391–403.

59. Resurgence of the Euler-MacLaurin summation formula, (with O. Costin), Annales de l’ Institut Fourier 58 (2008) 893–914.

60. Gevrey series in quantum topology, (with T.T.Q. Le), J. Reine Angew. Math., 618 (2008) 169–195.

61. Difference and differential equations for the colored Jones function, Journal of Knot Theory and its Ramifications, 17 (2008) 495–510.

62. The C-polynomial of a knot, (with X. Sun), Alg. Geom. Topology, 6 (2006) 1001–1031.

63. Is the Jones polynomial of a knot really a polynomial? (with T.T.Q. Le), Journal Knot ˆ Theory and its Ramifications, 15 (2006) 1–18.

64. Asymptotics of q-difference equations (with J. Geronimo), Contemporary Math. AMS 416 (2006) 83–114.

65. A non-commutative formula for the colored Jones function, (with M. Loebl), Math. Annalen, 336 (2006) 867–900.

66. Experimental evidence for the Volume Conjecture of the simplest hyperbolic non-2-bridge knot, (with Y. Lan), Algebr. Geom. Topol. 5 (2005) 379-403.

67. The colored Jones function is q-holonomic (with T.T.Q. Le), Geom. and Topology ˆ 9 (2005) 1253–1293.

68. A conjecture on Khovanov’s invariants, Fundamenta Mathematicae, 184 (2004) 99–101.

69. Nontriviality of the A-polynomial of knots in S 3 (joint with N. Dunfield), Alg. and Geom. Topology, 4 (2004) 1145–1153.

70. The quantum MacMahon Master Theorem (with T.T.Q. Le and D. Zeilberger), Proc. ˆ Natl. Academy USA, 103 (2006) 13928–13931.

71. Random walks and the colored Jones function (with M. Loebl), Combinatorica, 25 (2005) 651–671.

72. Whitehead doubling persists, Algebraic and Geometric Topology, 4 (2004) 935–942.

73. Finite type invariants of cyclic branched covers (with A. Kricker), Topology, 43 (2004) 1247–1283.

74. A rational noncommutative invariant of boundary links (with A. Kricker), Geometry and Topology, 8 (2004) 115–204.

75. The loop expansion of the Kontsevich integral, abelian invariants of knots and S-equivalence (with L. Rozansky), Topology, 43 (2004) 1183-1210.

76. On the characteristic and deformation varieties of a knot, Proceedings of the Casson Fest, Geometry and Topology Monographs 7 (2004) 291–309.

77. On knots with trivial Alexander polynomial (with P. Teichner), Journal of Diff. Geometry, 67 (2004) 763–789.

78. Tree-level invariants of 3-manifolds, Massey products and the Johnson homomorphism (with J. Levine), Graphs and Patterns in Mathematics and Theoretical Physics, Proceedings Symp. Pure Math. 73 (2005) 173–205.

79. The Arhus integral of rational homology 3-spheres III: The Relation with the Le-Murakami- ˚ Ohtsuki Invariant (D. Bar-Natan, L. Rozansky and D. Thurston), Selecta Math. 10 (2004) 305–324.

80. A surgery view of boundary links (with A. Kricker), Math. Annalen, 327 (2003) 103- 115.

81. Periodicity of Goussarov-Vassiliev knot invariants, Geom. and Topology Monographs, 4 (2002) 43–54.

82. Concordance and 1-loop clovers (with J. Levine), Algebraic and Geometric Topology, 1 (2001) 687–697.

83. Analytic invariants of boundary links (with J. Levine), Journal of Knot Theory and its Rami., 11 (2002) 283–293.

84. Homology surgery and invariants of 3-manifolds (with J. Levine), Geometry and Topology, 5 (2001) 551–578.

85. The mystery of the brane relation, Journal of Knot Theory and its Rami., 11 (2002) 725–738.

86. Calculus of clovers and finite type invariants of 3-manifolds (with M. Goussarov and M. Polyak), Geometry and Topology, 5 (2001) 75–108.

87. Signatures of links and finite type invariants of cyclic branched covers, Contemporary Math. 231 (1999) 87–97.

88. Applications of the lantern identity, Journal of Knot Theory and its Rami., 10 (2001) 303–307.

89. The Alexander polynomial and finite type 3-manifold invariants (with N. Habegger), Math. Annalen, 316 (2000) 485–497.

90. The Arhus integral of rational homology 3-spheres II: Invariance and Universality ˚ (with D. Bar-Natan, L. Rozansky and D. Thurston), Selecta Mathematica, 8 (2002) 341–371.

91. The Arhus integral of rational homology 3-spheres I: a highly non-trivial flat connection ˚ on S 3 (with D. Bar-Natan, L. Rozansky and D. Thurston), Selecta Mathematica, 8 (2002) 315–339.

92. Zeta functions at negative integers, Dedekind sums and toric geometry (with J. Pommesrsheim), Journal of AMS, 14 (2001) 1–23.

93. A reappearance of wheels, Journal of Knot Theory and its Rami., 7 (1998) 1065–1071.

94. Some IHX-type relations and symplectic representation theory (with H. Nakamura), Math. Research Letters 5 (1998) 391–402.

95. Wheels, wheeling and the Kontsevich integral of the unknot (with D. Bar-Natan, L. Rozansky and D. Thurston), Israel Journal of Mathematics, 119 (2000) 217–238.

96. Finite type 3-manifold invariants and the Torelli group I (with J. Levine), Inventiones Math. 131 (1998) 541–594.

97. Finite type 3-manifold invariants, the Torelli group and blinks (with J. Levine), Journal of Diff. Geometry, 47 (1997) 257–320.

98. On finite type 3-manifold invariants V: rational homology spheres (with T. Ohtsuki), Proceedings of the Aarhus Conference, Geometry and Physics, Marcel Dekker (1996) 445-457.

99. On finite type 3-manifold invariants IV: comparison of definitions (with J. Levine), Math. Proc. Cambridge Phil. Society 122 (1997) 291–300.

100. On finite type 3-manifold invariants III: manifold weight systems (with T. Ohtsuki), Topology 37 (1998) 227–244.

101. On finite type 3-manifold invariants II (with J. Levine), Math. Annalen 306 (1996) 691-718.

102. On finite type 3-manifold invariants I, Journal of Knot Theory and its Rami., 5 (1996) 441-462.

103. On the Melvin-Morton-Rozansky conjecture (with D.Bar-Natan), Inventiones Math. 125 (1996) 103-133.

104. Applications of TQFT invariants to low dimensional topology, Topology 37 (1998) 219– 224.

105. Relations among 3-manifold invariants, Thesis, Univ. of Chicago, 1992.

Submitted for publication

1. The Slope Conjecture for Montesinos knots (with R. van der Veen and C. Lee), preprint 2018, 1807.00957.

2. Bloch groups, algebraic K-theory, units and Nahm’s Conjecture, (with F. Calegari and D. Zagier), preprint 2017, arXiv:1712.04887.

3. Graph complexes and Mumford’s conjecture (with E. Getzler), preprint 2017, arXiv:1712.03606.

4. Non-peripheral ideal decompositions of alternating knots, (with I. Moffatt and D. Thurston), preprint 2016, arXiv:1610.09901.

5. A construction of the graphic matroid from the lattice of integer flows, (with Z. Dansco), preprint 2016, arXiv:1611.06282.

Preprints

1. Barriers, sweepouts and recognition of 3-manifolds, (with C. Hodgson and H. Rubinstein), preprint 2019.

2. Counting incompressible surfaces in 3-manifolds, (with N. Dunfield and H. Rubinstein), preprint 2019.

3. Counting genus 2 surfaces in 3-manifolds, (with N. Dunfield, C. Hodgson and H. Rubinstein), preprint 2018.

4. Knots, quantum modularity and perturbative series, (with D. Zagier), preprint 2019.

5. Knots and their related q-series, (with D. Zagier), preprint 2019.

6. The Newton polytope of a recurrent sequence of polynomials, preprint 2014.

7. The colored HOMFLY polynomial is q-holonomic, preprint 2012, arXiv:1211.6388.

8. q-terms, singularities and the extended Bloch group, preprint 2007, arXiv:0708.0018.

9. Resurgence of series of 1-dimensional sum-product type, (with O. Costin), preprint 2007.

10. On Chern-Simons Matrix Models, (with M. Marino), preprint 2005, ˜ arXiv:math/0601390.

11. Does the Jones polynomial determine the signature of a knot? preprint 2003, arXiv:math/0310203.

12. Beads: From Lie algebras to Lie groups, preprint 2002, arXiv:math/0201056.

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