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

Paul Halmos

Here is a list of my publications and preprints.

  1. A counterexample to the generalisation of Marché’s conjecture, e-print: arXiv:2205.01653.
  2. Kauffman bracket skein module of the connected sum of handlebodies: A counterexample, with J. H. Przytycki, Manuscripta Math. 167 (2022), no. 3-4, 809–820. DOI: 10.1007/s00229-021-01288-5, e-print: arXiv:2005.07750.
  3. On framings of links in 3-manifolds, with D. Ibarra, J. H. Przytycki, G. Montoya-Vega, D. Weeks, Canad. Math. Bull. 64 (2021), no. 4, 752–764. DOI: 10.4153/S000843952000079X, e-print: arXiv:2001.07782.
  4. A generalization of the Gram determinant of type A, with S. Mukherjee, D. Ibarra, J. H. Przytycki, Topology Appl. 295 (2021), Paper No. 107663, 15 pp., e-print: arXiv:1905.07834.
  5. Schur multipliers and second quandle homology, with S. Mukherjee D. Ibarra, T. Nosaka and J. H. Przytycki, J. Algebra 552 (2020), 52–67. DOI: 10.1016/j.jalgebra.2019.12.027, e-print: arXiv:1812.04704.
  6. On multiplying curves in the Kauffman bracket skein algebra of the thickened four–holed sphere, with S. Mukherjee, J. H. Przytycki, M. Silvero and X. Wang, J. Knot Theory Ramifications, 30 (2021), no. 14, Paper No. 2141001, 29 pp. DOI: 10.1142/S0218216521410017, e-print: arXiv:1805.06062.

Scholarly Books and Articles

  1. 2020: Lectures in knot theory: An Exploration of Contemporary Topics, Springer Universitext (in preparation, accepted for publication), with J. H. Przytycki, D. Ibarra, G. Montoya-Vega, and D. Weeks. 
  2. 2020: Chapter 63: Skein modules of 3-manifolds and Chapter 69: Kauffman bracket skein modules of 3-manifolds, with J. H. Przytycki and H. Wong, Encyclopedia of Knot Theory, Chapman and Hall/CRC Press (2020), DOI: 10.1201/9781138298217, ISBN: 9781138298217.