Published Articles

• The Generalized Kauffman-Harary Conjecture is True, with R. P. Bakshi, H. Guo, S. Mukherjee, J. H. Przytycki, Algebraic & Geometric Topology 25 (2025) 2067–2081. DOI: 10.2140/agt.2025.25.2067. e-print:arXiv:2301.02645 [math.GT].

• A Study of Gram Determinants in Knot Theory, with D. Ibarra, AMS Contemp. Math., 827 (2025), Special Session on Algebraic Structures in Knot Theory. Bookstore.ams.org. e-print:arXiv:2402.09704 [math.GT].

• A new Gram determinant from the Möbius band, with D. Ibarra, Journal of Knot Theory and Its Ramifications, Vol. 33, No. 12, 2450037 (2024). doi:10.1142/S0218216524500378. e-print:arXiv:2304.05616 [math.GT].

• An Initial Look to Knot Theory and Khovanov Homology, (Spanish), Rev. Integr. temas mat., 41(2), 103–123. https://doi.org/10.18273/revint.v41n2-2023003. e-print:arXiv:2308.10277 [math.HO].

• On Framings of Links in 3-Manifolds, with R. P. Bakshi, D. Ibarra, J. H. Przytycki, D. Weeks, Canadian Mathematical Bulletin. 2021;64(4):752-764. DOI: 10.4153/S000843952000079X. e-print:arXiv: 2001.07782 [math.GT]. 

Accepted Articles

• Alexander-Conway and bracket polynomials of a family of pretzel links, with A. Hernandez-Flores. e-print:arXiv:2412.20240 [math.GT]. (to appear in Rev. Integr. temas mat.).

• On the Khovanov Homology of T(2,n) Via Long Exact Sequence, (to appear in AMS Contemp. Math.). e-print:arXiv:2308.08452 [math.GT].

• On the notion of Khovanov A-adequacy, with L. Buchanan, H. Guo, M. Silvero, Y. Rong. e-print:arXiv:2502.17637 [math.GT].    (to appear in MATRIX Annals).

• Remarks on the Montesinos-Nakanishi 3-move conjecture, with R. P. Bakshi, B. Burton, H. Guo, D. Ibarra, S. Mukherjee, J. H. Przytycki. (to appear in MATRIX Annals).

• An unknotting robot, with C. Hui, D. Ibarra, L. Kauffman , E. McQuire, S. Mukherjee, C. Reid. (to appear in MATRIX Annals).

• Indepence Complexes of Circle Graphs, with R. P. Bakshi, H. Guo, D. Ibarra,  S. Mukherjee,  M. Silvero, J. Spreer. e-print:arXiv:2412.01125 [math.GT]. (to appear in MATRIX Annals). 

• Exploring unimodality of the plucking polynomial with delay function, with D. Ibarra, A. Landry, J. H. Przytycki, (to appear in AMS Contemp. Math.). e-print:arXiv:2311.18059 [math.GT].

Submitted Articles

• Chebyshev Polynomials and Gram Determinants from the Möbius Band, with A. Christiana and D. Ibarra. e-print:arXiv:2504.16439 [math.GT].

• A robot that unknots knots, with C. Hui, D. Ibarra, L. Kauffman , E. McQuire, S. Mukherjee, C. Reid. e-print:arXiv:2504.01254 [math.GT]. 

• The Montesinos-Nakanishi 3-move conjecture for links up to 20 crossings, with R. P. Bakshi, B. Burton, H. Guo, D. Ibarra, S. Mukherjee, J. H. Przytycki. e-print:arXiv:2502.17711 [math.GT]. 

• Temperley-Lieb Categories on Non-Orientable Surfaces, with D. Ibarra and B. Morris. e-print: arXiv:2506.14319 [math.CT].   

Theses

• A Historical Exploration of Knot Theory, Khovanov Homology, and Framing Changes of Links and Skein Modules. Thesis (Ph.D.)–The George Washington University. ProQuest LLC, Ann Arbor, MI, 2022. 118 pp. ISBN: 979-8845-45866-7. 

• Khovanov Homology for Almost Alternating Knots, MS Thesis, Puerto Rico, May 2017. Scholar.uprm.edu/20.500.11801/1020. 

• Acerca de las Normas Sobre los Espacios con Producto Interior Indefinido (On Norms on Undefined Inner Product Spaces). Biblioteca.uniatlantico. BS Degree project, Colombia, December 2013. 

Book

• Lectures in Knot Theory: An Exploration of Contemporary Topics, with J. H. Przytycki, R. P. Bakshi, D. Ibarra, D. Weeks. Springer Universitext, Springer International Publishing. 2024 March. DOI 10.1007/978-3-031-40044-5.