Nafaa Chbili

Nafaa Chbili's Home Page
Dr. Nafaa Chbili Professor Department of Mathematical Sciences United Arab Emirates University Al Ain Abu Dhabi UAE						Education: PhD, University of Paris 7, France, 1997. HDR, Monastir University, Tunisia, 2008. MSc, University of Paris 7, France, 1994. BSc, Monastir University, Tunisia, 1992.

Mathematical Genealogy (Academic tree): click here

Previous Appointments:

2007-2008. Max-Planck-Institute for Mathematics, Bonn, Germany

2006-2007. KAIST, Daejeon, South Korea

2005-2006. Osaka City Advanced Mathematical Institute, Osaka, Japan

2003-2005. Tokyo Institute of Technology, Tokyo, Japan,

1998-2003. Monastir University, Tunisia.

Teaching Spring 2023:

MATH145 Linear Algebra for Engineering:

Syllabus

Past Exams: Test1F23 ; Test2F2022 ; Test3F2022 ; FEF2022 ; Sol.FEF2022 ;

MATH105 Calculus 1:

Syllabus

Past Exams: Test1S15 ; Test1S16 ; Test2S15 ; Test2S16 ; Test3S16 ; MTF14 ; FEF14 ;

Mathematics Riddels and Chalenging Problems (open to all students):

Research Interests:

Low Dimensional Topology, Knot Theory and Applications.

Selected Publications:

Extensions of Braid Group Representations to the Monoid of Singular Braids, Mediterr. J. Math. 21, 180 (2024) (2024) (With V. Bardakaov and T. Kozlovskaya )

On quasi-alternating knots with symmetric union presentations, Osaka Journal of Mathematics (2024) (with T. Tanaka)
The Fox Trapezoidal Conjecture for Alternating Knots (a survey) Symmetry (2024) 16 (4).
Colored HOMFLY-PT polynomials of quasi-alternating 3-braid knots Nuclear Physics B, Volume 980, 2022, 115800 (2022) (with V. Singh) .
A Note on the Jones Polynomial of 3-braid links, Siberian Mathematical Journal 63, 983-994, (2022).
On the Khovanov Homology of quasi-alternating links, Mediterranean Journal of Mathematics, 19, 104, (2022) (with K. Qazaqzeh)
On Fox's Trapezoidal Conjecture for closed 3-braids, International Journal of Mathematics, Vol. 31, N. 14, (2021) (with M. Alrefai)
Extending Quasi-alternating links, Journal of Knot theory and Ramifications, Vol. 29, No. 11, 2050072 (2020) (with K. Kaur)
Extended periodic links and the HOMFLYPT polynomial, Journal of Knot Theory and Ramifications, (2019), 1940006 (with H. Jebali).
On the Jones Polynomial of Quasi-alternating Links. Topology and Its Applications, 264, (2019), pp. 1-11 (with K. Qazaqzeh).
Graph Polynomials and Symmetries, Journal of Algebra and Its Applications, (2019), 1950172
Ribbon graphs and the Temperley-Lieb algebra, AMS Contemporary Mathematics, 670 (2016) pp 299-312, American Mathematical Scociety.
A new obstruction of quasi-alternating links, Algebraic & Geometric Topology 15 (2015), no. 3, 1847-1862 (with K. Qazaqzeh).
Characterization of quasi-alternating Montesinos links, J. Knot Theory Ramifications, 24 (2015), no. 1, 1550002, 13 pp (with K. Qazaqzeh and B. Qublan).
Graph skein modules and symmetries of spatial graphs, J. Knot Theory Ramifications Vol. 21 No. 9 1250090 (2012).
Equivariant Khovanov homology associated with symmetric links, Kobe Journal of Mathematics, 27(2010) pp. 73-89.arxiv.org/abs/math.QA/0702359
Strong periodicity of links and the coefficients of the Conway polynomial, Proc. Amer. Math. Soc. 136 (2008), 2217-2224.
Toward an equivariant Khovanov homology, Proceedings of ILDT 2006, World Scientific Publishing Co, pp.19-27, 2007.

The Casson-Walker-Lescop invariant of periodic three-manifolds, Mathematical Proceeding Cambridge Philosophical Society , Vol. 140. (2006) pp. 253-264.
Skein algebras of the solid torus and symmetric spatial graphs, Fundamenta Mathematicae Vol 190, (2006) pp. 1-10.
Les invariants $\theta_{p}$ des 3-varietes periodiques, Ann. Inst. Fourier, 4 (2001), 1135-1150.
Symm'etries en dimension 3, une approche quantique, Cubo Math. Eud. Vol 6, No 4, (2004) pp. 133-165.
A new criterion for knots with free periods, Ann. Fac. Sci. Toulouse Math. (6) 12 (2003), no. 4, pp. 465-477.

Quantum invariants and finite group actions on 3-manifolds, Topology and its Applications, vol 136/1-3 pp. 219-231 2004.

The multivariable Alexander polynomial of lens braids, Journal of knot theory and its Ramifications, Vol 11, 8, pp.1323-1330,2002.

Quantum Su(3)-invariants of links and Murasugi's congruence, Topology and its Applications, Volume 122/3, pp. 479-485, 2002.

The skein polynomial of freely periodic knots, Topology and its Applications, Volume 121/3 pp. 535-542, 2002.

The Jones polynomials of freely periodic knots, Journal of Knot Theory and its Ramifications, Vol 9, No 7, pp. 885-891, 2000.

Le polynome de Homfly des noeuds librement periodiques, C. R. Acad. Sci. Paris, t. 325,b Serie I, pp. 411-414, 1997.

On the invariants of lens knots, proceeding of knots 96,c-1997 World scientific publishing Co, pp. 365-375.

Some Links

Knots and Spatial Graphs 2024, UAE University, November 4-8, 2024
Workshop Knots + More, KAIST, Daejeon, Korea, August 18-25, 2021
DNA Topology Course-Workshop, Okinawa, Japan, November 2-7, 2009 (co-organized with Robert Sinclair)

Second Tapu-Kook joint seminar on knots and related Topics, Daegu, Korea, July 26-30 2010

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