Thang Le
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160,
USA
Email: letu@math.gatech.edu
Publications
Research papers
- Quantum
trace for SL_n-skein algebras,
with T. Yu, preliminary
version. Your comments are very welcome.
- Stated SL(n)-Skein Modules and Algebras,
with A. Sikora, Preprint arXiv 2201.00045.
- Root of unity quantum cluster algebras
and Cayley-Hamilton algebras,
with S Huang and M. Yakimov. Preprint arXiv:2107.11926.
- Faithfulness of geometric action of
skein algebras. Preprint arXiv:2103.11532.
- Quantum traces and embeddings
of stated skein algebras into quantum tori, with T. Yu. Preprint arXiv:2012.15272. Link to pdf.
- The Chebyshev-Frobenius
Homomorphism for stated skein modules of 3-manifolds, with
W. Bloomquist, Math Zeitschrift, to apprear.
Preprint arXiv:2011.02130. Link to Pdf
- SL_2
quantum trace in quantum Teichmuller
theory via writhe, With H. K. Kim and M. Son, Algebr. Geom. Topol,
to appear. Preprint Arxiv:1812.11628.
(new, updated version). Link to Pdf
file.
- Stated skein modules of marked
3-manifolds/surfaces, a survey, With T. Yu, Acta
Math. Vietnam. 46
(2021),
no.
2, 265–287. pdf
- Lower and upper bounds for positive
bases of skein algebras. With D. Thurston and T. Yu. Int.
Math. Res. Not. IMRN 2021, no.
4, 3186-3202. Link to pdffile
- Stated skein algebras of
surfaces. With F. Costantino. Journal of EMS, to appear. Preprint arXiv:1907.11400,
2019. New version pdf.
- Dimension and Trace of the
Kauffman Bracket Skein Algebra, With C. Frohman and J. Kania-Bartoszynska. Trans.
Amer. Math. Soc. Ser. B 8
(2021),
510–547. Link to pdf.
- On Kauffman bracket skein modules of marked 3-manifolds
and the Chebyshev-Frobenius homomorphism. With J. Paprocki. Algebr. Geom. Topol.
19
(2019),
no.
7, 3453-3509. Link to pdf.
- Unicity for Representations of the Kauffman bracket
Skein Algebra. With C. Frohman and J. Kania-Bartoszynska. Invent.
Math. 215
(2019),
no.
2, 609-650. pdf.
- Triangular decomposition of skein algebras, Quantum Topology, 9 (2018), 591-632. Link to pdf.
- The colored Homflypt function
is q-holonomic.
With S. Garoufalidis and A. Lauda. Duke Math. Journal, 167, Number 3 (2018), 397-447. Link to pdf.
- 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,
18 (2019), no. 2,
249-291.
- 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. .pdf
- 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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