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

March 2023

February 2023

January 2023

December 2022

Selected Publications:

1. BPS spectra of complex knots, Physical Review D 111, 106011 (2025) (with V. Singh)
2. Extensions of Braid Group Representations to the Monoid of Singular Braids, Mediterr. J. Math. 21, 180 (2024) (with V. Bardakov and T. Kozlovskaya)
3. On quasi-alternating knots with symmetric union presentations, Osaka J. Math. 62(2), 317-328 (2025) (with T. Tanaka)
4. On the Jones polynomial of quasi-alternating links II, Osaka J. Math. 62(2), 221-231 (2025) (with K. Qazaqzeh and A. Alrhayyal)
5. The Fox Trapezoidal Conjecture for Alternating Knots (a survey), Symmetry 16(4), 2024
6. Colored HOMFLY-PT polynomials of quasi-alternating 3-braid knots, Nucl. Phys. B 980, 115800 (2022) (with V. Singh)
7. A Note on the Jones Polynomial of 3-braid links, Siberian Math. J. 63, 983-994 (2022)
8. On the Khovanov Homology of quasi-alternating links, Mediterr. J. Math. 19, 104 (2022) (with K. Qazaqzeh)
9. On Fox's Trapezoidal Conjecture for closed 3-braids, Int. J. Math. 31(14), 2021 (with M. Alrefai)
10. Extending Quasi-alternating links, J. Knot Theory Ramifications 29(11), 2050072 (2020) (with K. Kaur)
11. Extended periodic links and the HOMFLYPT polynomial, J. Knot Theory Ramifications, 1940006 (2019) (with H. Jebali)
12. On the Jones Polynomial of Quasi-alternating Links, Topology Appl. 264 (2019), 1-11 (with K. Qazaqzeh)
13. Graph Polynomials and Symmetries, J. Algebra Appl. (2019), 1950172
14. Ribbon graphs and the Temperley–Lieb algebra, Contemp. Math. 670 (2016), 299-312
15. A new obstruction of quasi-alternating links, Algebr. Geom. Topol. 15(3) (2015), 1847-1862 (with K. Qazaqzeh)
16. Characterization of quasi-alternating Montesinos links, J. Knot Theory Ramifications 24(1), 1550002 (2015) (with K. Qazaqzeh and B. Qublan)
17. Graph skein modules and symmetries of spatial graphs, J. Knot Theory Ramifications 21(9), 1250090 (2012)
18. Equivariant Khovanov homology associated with symmetric links, Kobe J. Math. 27 (2010), 73-89. arXiv
19. Strong periodicity of links and the coefficients of the Conway polynomial, Proc. AMS 136 (2008), 2217-2224
20. Toward an equivariant Khovanov homology, Proc. ILDT 2006, World Scientific, 19-27 (2007)
21. The Casson-Walker-Lescop invariant of periodic three-manifolds, Math. Proc. Camb. Phil. Soc. 140 (2006), 253-264
22. Skein algebras of the solid torus and symmetric spatial graphs, Fund. Math. 190 (2006), 1-10
23. Les invariants θ_p des 3-variétés périodiques, Ann. Inst. Fourier 51(4), 1135-1150 (2001)
24. A new criterion for knots with free periods, Ann. Fac. Sci. Toulouse (6) 12(4), 465-477 (2003)
25. Quantum invariants and finite group actions on 3-manifolds, Topology Appl. 136 (2004), 219-231
26. The multivariable Alexander polynomial of lens braids, J. Knot Theory Ramifications 11(8), 1323-1330 (2002)
27. Quantum SU(3)-invariants of links and Murasugi's congruence, Topology Appl. 122(3), 479-485 (2002)
28. The skein polynomial of freely periodic knots, Topology Appl. 121(3), 535-542 (2002)
29. The Jones polynomials of freely periodic knots, J. Knot Theory Ramifications 9(7), 885-891 (2000)
30. Le polynôme de HOMFLY des nœuds librement périodiques, C. R. Acad. Sci. Paris 325(I), 411-414 (1997)
31. On the invariants of lens knots, Proc. Knots 96, World Scientific, 365-375 (1997)