Thang Le
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160, USA
Email: letu@math.gatech.edu

Publications

Research papers

Dimension and Trace of the Kauffman Bracket Skein Algebra, With C. Frohman and J. Kania-Bartoszynska. Preprint ArXiv:1902.02002, 2019. pdf
On Kauffman bracket skein modules of marked 3-manifolds and the Chebyshev-Frobenius homomorphism. With J. Paprocki. Preprint arXiv:1804.09303, 2018. pdf.
Unicity for Representations of the Kauffman bracket Skein Algebra. With C. Frohman and J. Kania-Bartoszynska. Inventiones Mathematicae (2018). DOI 10.1007/s00222-018-0833-x. Here is a pdf.
Triangular decomposition of skein algebras, Quantum Topology, 9 (2018), 591-632. pdf.
The colored Homflypt function is q-holonomic. With S. Garoufalidis and A. Lauda. pdf. Duke Math. Journal, 167, Number 3 (2018), 397-447.
On positivity of Kauffman bracket skein algebras of surfaces, International Mathematics Research Notices, 2018, no. 5, 1314-1328. pdf.
A survey of q-holonomic functions. With S. Garoufalidis. Preprint arXiv:1601.07487, 2016, pdf. L'Enseignement Mathematique, 62 (2016), no. 3-4, 501-525.
Quantum Teichmuller spaces and quantum trace map, preprint arXiv:1511.06054, 2015, pdf. Journal of the Institute of Mathematics of Jussieu, to appear.
Unified quantum invariants for integral homology spheres associated with simple Lie algebras. With K. Habiro. Geometry and Topology 20 (2016), 2687-2835. DOI 10.2140/gt.2016.20.2687. pdf
Character varieties, A-polynomials, and the AJ Conjecture. With Xingru Zhang. pdf . Algebraic & Geometric Topology, 17 (2017), no. 1, 157-188.
The colored Jones polynomial and the AJ conjecture. Lecture notes from "Etats de la Recherche : Geometric and quantum topology in dimension 3" at the CIRM in Luminy, July 2014. pdf. Appeared in in ``Lectures on quantum topology in dimension three" (by T. Le, C. Lescop, R. Lipshitz, P. Turner), Panoramas et Syntheses, N 48 (2016), Soc. Math. France, pp 33-90.
Growth of homology torsion in finite coverings and hyperbolic volume. Preprint arXiv:1412.7758, 2014. pdf. Annales de l'Institut Fourier, 68 (2018), no. 2, 611--645.
On Kauffman Bracket Skein Modules at Root of Unity. Algebraic & Geometric Topology, 15 (2015), no. 2, 1093-1117. pdf
Nahm sums, stability and the colored Jones polynomial. With S. Garoufalidis. Research in Mathematical Sciences, 2 (2015), Art. 1, 55 pp. pdf
On the AJ conjecture for knots. With Anh Tran. Indiana Univ. Math. J. 64 (2015), no. 4, 1103-1151. pdf
Homology torsion growth and Mahler measure. Comment. Math. Helv. 89 (2014), no. 3, 719-757. pdf
On the integrality of the Witten-Reshetikhin-Turaev 3-manifold invariants. With A. Beliakova and Q. Chen. Quantum Topology 5 (2014), 99-141 .pdf
The skein module of two-bridge links. With Anh Tran. Proceedings Amer. Math. Soc. 142 (2014), 1045-1056. pdf
Growth of regulators in finite abelian coverings. Algebraic & Geometric Topology 13 (2013), 2383-2404. pdf
The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant. With T. Kuriya and T. Ohtsuki. J. Topology 5 (2012), 458--484. pdf
On the unification of quantum 3-manifold invariants. With A. Beliakova, in "Introductory lectures on knot theory", Ser. Knots Everything 46, World Sci. Publ., Hackensack, NJ, 2012, 1--21, .pdf
Asymptotics of the colored Jones function of a knot. With S. Garoufalidis. Geometry and Topology, 15 (2011), 2135-2180. .pdf
Unified SO(3) Quantum Invariants for Rational Homology 3-Spheres. With A. Beliakova and I. Buehler, Invent. Math. 185 (2011), 121-174. .pdf
On the Volume Conjecture for Cables of Knots. With Anh Tran. J. Knot Theory Ramifications, 19 (2010), 1673--1691. .pdf
Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion. With A. Beliakova and C. Blanchet. Fund. Math. 201 (2008), 217-239. .pdf
Analyticity of the free energy of a closed 3-manifold. With S. Garoufalidis and M. Marino. Symmetry, Integrability and Geometry: Methods and Applications, 4 (2008), 080, 20 pages (electronic). .pdf
Strong Integrality of Quantum Invariants of 3-manifolds. Trans. Amer. Math. Soc. 360 (2008), 2941-2963. .pdf
Twisted Alexander Polynomial of links in the projective space. With Vu Huynh. Knot Theory Ramifications 17 (2008), 411-438. pdf
Gevrey series in quantum topology. With S. Garoufalidis. J. Reine Angew. Math. 618 (2008), 169-195. .pdf
Integrality of quantum 3-manifold invariants and a rational surgery formula. With A. Beliakova. Compositio Mathematica, 143 (2007), 1593-1612. .pdf
A TQFT associated to the LMO invariant of three-dimensional manifolds. With D. Cheptea. Comm. Math. Phys. 272 (2007), 601-634. pdf
Is the Jones polynomial of a knot really a polynomial? With S. Garoufalidis. J. Knot Theory and its Ramification 15 (2006), 983--1000. pdf
The Colored Jones Polynomial and the A-Polynomial of Knots. Adv. in Math. 207 (2006), 782--804 .pdf . Corrections.
The quantum MacMahon Master Theorem. With S. Garoufalidis and D. Zeiberger. Proceedings of the Nat. Acad. Sci. 103 (2006), N 38, 13928--13931. pdf.
On the Colored Jones Polynomial and the Kashaev invariant. With Vu Huynh. Fundam. Prikl. Mat. 11 (2005), no. 5, 57-78. pdf
Almost integral TQFTs from simple Lie algebras. With Q. Chen. Algebr. Geom. Topol. 5 (2005), 1291--1314. pdf
The colored Jones function is q-holonomic. With S. Garoufalidis. Geom. Topol. 9 (2005), 1253--1293. pdf
Quantum Invariants of Periodic Links and Periodic 3-Manifolds. With Q. Chen. Fund. Math. 184 (2004), 55--71. pdf
Quantum groups and ribbon G-categories. With V. Turaev. J. Applied and Pure Algebra 178 (2003), 169--185. pdf
Two applications of elementary knot theory to Lie algebras and Vassiliev invariants. With D. Bar-Natan and D. Thurston. Geometry and Topology, 7 (2003), 1-31. pdf
Quantum 3-manifolds invariants: integrality, splitting, and perturbative expansion. Topology and its applications, 127 (2003), 125-152. .pdf
Integrality and symmetry of quantum link invariants. Duke Math. J. 102 (2000), no. 2, 273--306. pdf
On the perturbative PSU(n) invariants of rational homology 3-spheres. Topology 39 (2000), no. 4, 813-849. .p df
3-manifold invariant derived from the Kontsevich integral. With J. Murakami, H. Murakami, T. Ohtsuki. Osaka J. Math. 36 (1999), no. 2, 365--395.
On the denominators of the Kontsevich integral and the universal perturbative invariant. Invent. Math. 135 (1999), no. 3, 689-722. .pdf
A universal perturbative invariant of 3-manifolds. With J. Murakami and T. Ohtsuki. Topology, 37 (1998), 539--574. pdf
The parallel version of the Kontsevich integral. With J. Murakami.J. Pure and Applied Algebra, 121 (1997), 271--291. .pdf
An invariant of integral homology 3-spheres which is universal for all finite types invariants. In ``Soliton, Geometry, and Topology: On the Crossroad'', AMS Translations series 2, 179 (1997) Eds. V. Buchstaber and S. Novikov, pp. 75-100. .pdf
Local rules for quasiperiodic tilings. In "The mathematics of long-range aperiodic order", NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 489, Kluwer Acad. Publ., Dordrecht, 1997. pp 331-366. pdf
A quantum $sl_2$-invariant of 3-manifolds which contains all the Witten-Reshetikhin-Turaev invariants. Lect. Notes in Pure and Appl. Math. 184, Marcel Dekker Inc. 1996. Eds. J. E. Andersen, J. Dupont, H. Pedersen and A.Swann, 399-409. .pdf
The Universal Vassiliev-Kontsevich Invariant for framed oriented links. With J. Murakami. Compositio Mathematics 102 (1996), pp. 41--64. pdf
The Kontsevich integral for Kauffman's polynomials. With J. Murakami. Nagoya Mathematical Journal, {\bf 142} (1996), pp. 39--66.
A 3-manifold invariant derived from the universal Vassiliev-Kontsevich invariant. With J. Murakami, H. Murakami, T. Otsuki. Proceeding of the Japan Academy, series A, Mathematical Sciences LXXI (1995), ser. A, N 6, pp. 125--127.
Representation of the category of Tangles by Kontsevich iterated integrals. With J. Murakami. Commun. Math. Physics 168 (1995), 535-562. .pdf
Kontsevich's integrals for Homfly polynomials and relations between multiple zeta values. With J. Murakami. Topology and its Applications, 62 (1995), 193--206. pdf
Local rules for pentagonal quasiperiodic tilings. Discrete and Computational Geometry, 14 (1995), 31-70. pdf
Local rules for multidimensional quasiperiodic tilings. With S. Piunikhin. Differential Geometry and its applications, 5 (1995), 13-31. pdf
The geometry of quasicrystals. With S. Piunikhin and V. Sadov. (Russian) Uspekhi Mat. Nauk 48 (1993) , 41-102; translation in Russian Math. Surveys 48 (1993), no. 1, 37-100.
Varieties of representations and their subvarieties of cohomology jumps for knot groups. (Russian) Mat. Sb. 184 (1993), no. 2, 57--82; translation in Russian Acad. Sci. Sb. Math. 78 (1994), no. 1, 187-209. pdf
Local rules for quasiperiodic tilings of quadratic 2-planes in R^4. With S. Piunikhin and V. Sadov. Commun. Math. Phys. 150 (1992), 23-44. pdf
Varieties of representations and their subvarieties of cohomology jumps for certain knot groups. (Russian) Uspekhi Mat. Nauk 46 (1991), no. 2(278), 223-224; translation in Russian Math. Surveys 46 (1991), no. 2, 250--251.
Novikov's numbers. (Russian) Mat. Zametki 47 (1990), no. 1, 98-104; translation in Math. Notes 47 (1990), no. 1-2, 64-68.
Structure of level surfaces of closed 1-forms. (Russian) Mat. Zametki 44 (1988), no. 1, 124--133; translation in Math. Notes 44 (1988), no. 1-2, 556-562.

Others

Finite type invariants of 3-manifolds. In ``Encyclopedia of Mathematical Physics", pp 384-356, Elsevier 2006. pdf
Lectures on the LMO invariant. Lectures given at the Grenoble 1999 Summer School on invariants of 3-manifolds. pdf
Aktueller Forschungsschwerpunkt: Invarianten von Knoten. With M. Kontsevich. In ``Max-Planck-Gesellschaft Jahrbuch 1994", pp 451--455. Max-Planck-Gesellschaft. pdf

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