Dr. M. Prabhakar – Department of Mathematics

Dr. M. Prabhkar

Associate Professor

Dr Prabhakar is an Associate Professor in the Department of Mathematics at IIT Ropar. After obtaining his doctoral degree from IIT Delhi, he carried out post-doctoral studies at Harish Chandra Research Institute, Allahabad. He was also a visiting research fellow at Osaka City University (Japan). Dr. Prabhakar was a faculty member in the Department of Mathematics at IIT Guwahati from March 2006 to July 2009.

Areas of Research:

Knot Theory
Spatial Graphs

Associate Professor, Indian Institute of Technology Ropar, India, December 2015 – at present
Assistant Professor, Indian Institute of Technology Ropar, India, 2009 – December 2015
Senior Lecturer, Indian Institute of Technology Guwahati, India, 2006-09
Visiting Researcher, Osaka City University, Osaka, Japan, 2006
Post-Doctoral Fellow, HRI, Allahabad, India, 2005-06
Teaching Assistant, Indian Institute of Technology Delhi, India, 2000-05

1. Komal Negi, Ayaka Shimizu, Yoshiro Yaguchi, and Madeti Prabhakar, Orbits by the up–down action of braid diagrams, Journal of Knot Theory and Its Ramifications, Vol. 34, No. 08, 2550031, 2025
2. K. Negi, A. Shimizu, M. Prabhakar, Warping Labeling for twisted knots and twisted virtual braids, Tokyo Journal of Mathematics, Vol. 48, No. 2, 2025
3. V. Bardakov, T. Kozlovskaya, K. Negi, and M. Prabhakar, Twisted virtual braid group, Journal of knot theory and its ramifications, (https://doi.org/10.1142/S0218216525500282), 2025
4. K. Negi and M. Prabhakar, Generalization of Arc Shift for twisted knots, Journal of knot theory and its ramifications, Vol. 33, No. 02, 2450004, 2024
5. K. Negi and M. Prabhakar, Singular twisted links and Singular twisted virtual braids, International Journal of Mathematics, (https://doi.org/10.1142/S0129167X25500211), 2025.
6. Kirandeep Kaur, and Prabhakar Madeti, Virtual Knots and Links with Unknotting index (n,m), Bulletin of the Korean Mathematical Society, (https://doi.org/10.4134/BKMS.b240494) 2025.
7. K. Negi, M. Prabhakar, and S. Kamada, “Twisted virtual braids and twisted links,” Osaka Journal of Mathematics, vol. 61-4, 2024.
8. S. Joshi, K. Negi, and M. Prabhakar, “Some evaluations of the Jones polynomial for certain families of weaving knots,” Topology Appl., vol. 329, Paper No. 108466, 11, 2023.
K. Negi and M. Prabhakar, “Numerical invariants for two-component virtual spatial graphs,” Journal of Topology and Analysis, vol. Online Ready, Paper No. 1–13, (doi: 10.1142/S1793525323500310), 2023.
10. A. Gill, M. Ivanov, M. Prabhakar, and A. Vesnin, “Recurrent generalization of f-polynomials for virtual knots and links,” Symmetry, vol. 14, no. 1, pp. 1–15, (doi: 10.3390/sym14010015), 2022.
11. A. Gill and P. Madeti, “Variations in writhes of virtual knots under a local move,” Bull. Korean Math. Soc., vol. 59, no. 2, pp. 303–318, 2022, issn: 1015-8634,2234-3016. doi: 10.4134/BKMS.b200927.
12. S. Joshi and M. Prabhakar, “Determinants of twisted generalized hybrid weaving knots,” J. Knot Theory Ramifications, vol. 31, no. 14, Paper No. 2250104, 10, 2022, issn: 0218-2165,1793-6527. doi: 10.1142/S0218216522501048.
13. A. Gill, K. Kaur, M. Prabhakar, and A. Vesnin, “An unknotting invariant for welded knots,” Proc. Indian Acad. Sci. Math. Sci., vol. 131, no. 2, Paper No. 47, 17, 2021, issn: 0253-4142,0973-7685. doi: 10.1007/s12044-021-00640-9.
14. S. Joshi and M. Prabhakar, “The Gordian complex of theta-curves,” J. Knot Theory Ramifications, vol. 30, no. 8, Paper No. 2150050, 11, 2021, issn: 0218-2165,1793-6527. doi: 10.1142/S0218216521500504.
15. A. Gill, M. Prabhakar, and A. Vesnin, “Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves,” J. Knot Theory Ramifications, vol. 29, no. 10, pp. 2042008, 24, 2020, issn: 0218-2165,1793-6527. doi: 10.1142/S0218216520420080.
16. A. Gill, K. Kaur, and P. Madeti, “Arc shift number and region arc shift number for virtual knots,” J. Korean Math. Soc., vol. 56, no. 4, pp. 1063–1081, 2019, issn: 0304-9914,2234-3008. doi: 10.4134/JKMS.j180615.
17. K. Kaur, M. Prabhakar, and A. Vesnin, “An unknotting index for virtual links,” Topology Appl., vol. 264, pp. 352–368, 2019, issn: 0166-8641,1879-3207. doi: 10.1016/j.topol.2019.06.030.
18. K. Kaur, S. Kamada, A. Kawauchi, and P. Madeti, “An unknotting index for virtual knots,” Tokyo J. Math., vol. 42, no. 2, pp. 357–370, 2019, issn: 0387-3870. doi: 10.3836/tjm/1502179283.
19. K. Kaur, M. Prabhakar, and A. Vesnin, “Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants,” J. Knot Theory Ramifications, vol. 27, no. 13, pp. 1842015, 22, 2018, issn: 0218-2165,1793-6527. doi: 10.1142/S0218216518420154.
20. K. Kaur, S. Kamada, A. Kawauchi, and M. Prabhakar, “Gauss diagrams, unknotting numbers and trivializing numbers of spatial graphs,” Topology Appl., vol. 230, pp. 586–598, 2017, issn: 0166-8641,1879-3207. doi: 10.1016/j.topol.2017.08.037.
21. V. Siwach and M. Prabhakar, “On minimal unknotting crossing data for closed toric braids,” Kyungpook Math. J., vol. 57, no. 2, pp. 331–360, 2017, issn: 1225-6951,0454-8124. doi: 10.5666/KMJ.2017.57.2.331.
22. V. Siwach and P. Madeti, “An unknotting sequence for torus knots,” Topology Appl., vol. 196, pp. 668–674, 2015, issn: 0166-8641,1879-3207. doi: 10.1016/j.topol.2015.05.065.
23. V. Siwach and P. Madeti, “Region unknotting number of 2-bridge knots,” J. Knot Theory Ramifications, vol. 24, no. 11, pp. 1550053, 20, 2015, issn: 0218-2165,1793-6527. doi: 10.1142/S0218216515500534.
24. S. Vikash and M. Prabhakar, “A sharp upper bound for region unknotting number of torus knots,” J. Knot Theory Ramifications, vol. 22, no. 5, pp. 1350019, 21, 2013, issn: 0218-2165,1793-6527. doi: 10.1142/S0218216513500193.
25. P. Madeti and R. Mishra, “Minimal degree sequence for torus knots of type (p, q),” J. Knot Theory Ramifications, vol. 18, no. 4, pp. 485–491, 2009, issn: 0218-2165,1793-6527. doi: 10.1142/S021821650900704X.
26. M. Prabhakar, “A bound on the unknotting number,” Int. J. Math. Anal., vol. 3, no. 5-8, pp. 339–345, 2009, issn: 1312-8876,1314-7579.
27. M. Prabhakar and R. Mishra, “Polynomial representation for long knots,” Int. J. Math. Anal., vol. 3, no. 5-8, pp. 325–337, 2009, issn: 1312-8876,1314-7579.
28. P. Madeti and R. Mishra, “Minimal degree sequence for 2-bridge knots,” Fund. Math., vol. 190, pp. 191–210, 2006, issn: 0016-2736,1730-6329. doi: 10.4064/fm190-0-7
29. P. Madeti and R. Mishra, “Minimal degree sequence for torus knots of type (p, 2p − 1),” J. Knot Theory Ramifications, vol. 15, no. 9, pp. 1141–1151, 2006, issn: 0218-2165,1793-6527. doi: 10.1142/S021821650600497X
30. A. Sahore, K. Negi, A. S. Gill, M. Prabhakar, Classification of virtual links by arc shift move, arXiv:2502.08955, 2024. (submitted)
31. Mohamad N. Nasser, Vaibhav Keshari, Madeti Prabhakar, Matrix representations of the twisted virtual braid group and its extensions, https://arxiv.org/abs/2506.03806, 2025 (submitted)
32. K. Negi, M. Prabhakar, The monoid structure of singular twisted virtual braids, arXiv:2502.08965, 2025. (submitted)
33. K. Kaur, A. Gill, and P. Madeti, “Arc shift number for some virtual knots,” Trends in Mathematics, (DOI:10.1007/978-981-13-5742-8_6), 2019
34. S. Vikash and M. Prabhakar, “Exact unknotting sequence of torus knots,” in International Conference on Topology and Geometry, Japan-Mexico Topology Symposium, Japan, 2013, pp. 38–49.
35. M. Prabhakar and M. Rama, “Polynomial representation for links,” in Proceedings of Knot Theory for Scientific Objects, Osaka, Japan, 2007, pp. 143–154. 3
36. M. Prabhakar and M. Rama, “A degree sequence for general knot,” in Proceedings of Konan University, Konan University, 2005, pp. 169–178.
37. M. Prabhakar and M. Rama, “Minimal degree sequence for torus knots,” in Proceedings of Workshop on Topology of Knots, Nihon University, 2004, pp. 38–49.