Research

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

Paul Halmos

Here is a list of my publications and preprints. The years indicate when the results in the papers were proven.

  1. 2020: Kauffman bracket skein module of the connected sum of handlebodies: A counterexample, with J. H. Przytycki, Manuscripta Math. (to appear), e-print: arXiv:2005.07750.
  2. 2020: On framings of links in 3-manifolds, with D. Ibarra, J. H. Przytycki, G. Montoya-Vega, D. Weeks, Canad. Math. Bull. DOI: 10.4153/S000843952000079X, e-print: arXiv:2001.07782.
  3. 2019: A Generalization of the Gram determinant of type A, with S. Mukherjee, D. Ibarra, J. H. Przytycki, e-print: arXiv:1905.07834 (submitted).
  4.  2018: 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.
  5. 2018: 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 (to appear), 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).