Research

“The only way to learn mathematics is to do mathematics.”

Paul Halmos

Here are the links to my ResearchGate, Orcid, and Google Scholar pages.

Publications and Preprints

  1. R. P. Bakshi, A. Christiana, H. Guo, D. Ibarra, L. H. Kauffman, G. Montoya-Vega, S. Mukherjee, J. H. Przytycki, X. Wang, Fundamentals of cubic skein modules, e-print: arXiv:2511.10959 .
  2. R. P. Bakshi,  B. A. Burton, H. Guo, D. Ibarra, G. Montoya-Vega, S. Mukherjee, J. H. Przytycki, The Montesinos-Nakanishi 3-move conjecture for links up to 20 crossings, e-print: arXiv:2502.17711.
  3. R. P. Bakshi, S. Kim, S. Shi, X. Wang, On the Kauffman bracket skein module of (S1 × S2) # (S1 × S2), Journal of Algebra 673 (2025), 103–137, e-print: arXiv:2405.04337.
  4. R. P. Bakshi, H. Guo, G. Montoya-Vega, S. Mukherjee, and J. H. Przytycki, The generalized Kauffman-Harary conjecture is true, Algebraic and Geometric Topology 25 (2025), no. 4, 2067–2081, e-print: arXiv:2301.02645.
  5. R. P. Bakshi, A counterexample to the generalisation of Witten’s conjecture, Contemporary Mathematics 824, American Mathematical Society, [Providence], RI, 2025, 73–82., e-print: arXiv:2205.01653.
  6. R. P. Bakshi and J. H. Przytycki, Kauffman bracket skein module of the connected sum of handlebodies: A counterexample, Manuscripta Mathematica 167 (2022), no. 3-4, 809–820. e-print: arXiv:2005.07750.
  7. R. P. Bakshi, D. Ibarra, J. H. Przytycki, G. Montoya-Vega, and D. Weeks, On framings of links in 3-manifolds, Canadian Mathematical Bulletin 64 (2021), no. 4, 752–764. e-print: arXiv:2001.07782.
  8. R. P. Bakshi, S. Mukherjee, D. Ibarra, and J. H. Przytycki, A generalization of the Gram determinant of type A, Topology and its Applications 295 (2021), Paper No. 107663, 15 pp. e-print: arXiv:1905.07834.
  9. R. P. Bakshi, S. Mukherjee, D. Ibarra, T. Nosaka, and J. H. Przytycki, Schur multipliers and second quandle homology, Journal of Algebra 552 (2020), 52–67. e-print: arXiv:1812.04704.
  10. R. P. Bakshi, S. Mukherjee, J. H. Przytycki, M. Silvero, and X. Wang, On multiplying curves in the Kauffman bracket skein algebra of the thickened four–holed sphere, Journal of Knot Theory and its Ramifications, 30 (2021), no. 14, Paper No. 2141001, 29 pp. e-print: arXiv:1805.06062.

Scholarly Books and Encyclopedia Articles

  1. J. H. Przytycki, R. P. Bakshi, D. Ibarra, G. Montoya-Vega, and D. Weeks, Lectures in knot theory: An exploration of contemporary topics, Universitext Springer, Cham, 2024, xv+520 pp. ISBN: 978-3-031-40043-8; 9783031400445.
  2. R. P. Bakshi, J. H. Przytycki and H. Wong, Chapter 63: Skein modules of 3-manifolds, Encyclopedia of Knot Theory, Chapman and Hall/CRC Press (2020) pp. 617-623, ISBN: 9781138298217.
  3. R. P. Bakshi, J. H. Przytycki and H. Wong, Chapter 69: Kauffman bracket skein modules of 3-manifolds, Encyclopedia of Knot Theory, Chapman and Hall/CRC Press (2020), pp. 657-666, ISBN: 9781138298217.

Workshop Collaborations

  1. R. P. Bakshi, H. Guo, D. Ibarra, G. Montoya-Vega, S. Mukherjee, M. Silvero, J. Spreer, Matrix Project: Independence complexes of circle graphs, MATRIX Annals (to appear), e-print: arXiv:2412.01125.
  2. R. P. Bakshi, B. A. Burton, H. Guo, D. Ibarra, G. Montoya-Vega, S. Mukherjee, and J. H. Przytycki, MATRIX Project: Remarks on the Montesinos-Nakanishi 3-move conjecture, MATRIX Annals (to appear).