Thang T. Q. Le
(Lê Tự Quốc
Thắng)
Professor
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160,
USA
Tel:


(404)385-0054
FAX: (404)894-4409
Email: letu@math.gatech.edu

Research Interests: Differential topology, 3-manifolds, knot
theory, quasicrystals.
+ Recent preprints,
papers, talks, etc...

Teaching:
+ Please visit
Canvas for course syllabus and information.

Services:
+ Managing Editor, Quantum Topology. Papers
are submitted to The European Mathemathical Society
Publishing House at this
site.
+ Editor
for The Journal of
Knot theory and its Ramifications. Papers are submitted to World Scientific
at this site.
+ Editor
for Acta Mathematica
Vietnamica. Papers are submitted to Springer at this site.

New: I am co-organizing Conference “Quantum
Topology and Hyperbolic Geometry Conference” Da Nang,
Vietnam during May 27-31, 2019. Following the conference, there will be a workshop
consisting of 3 min-courses held at Quy Nhon University.

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
Teichmüller 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. Preprint arXiv:1804.09303, 2018. 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. 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,
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.
a.
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