Published Articles
A robot that unknots knots, with C. Hui, D. Ibarra, L. Kauffman , E. McQuire, S. Mukherjee, C. Reid, Journal of Knot Theory and Its Ramifications. doi:10.1142/S0218216526500021. e-print:arXiv:2504.01254 [math.GT].
Alexander-Conway and bracket polynomials of a family of pretzel links, with A. Hernandez-Flores, Rev. Integr. Temas Mat., 43 (2025), No. 2, 27–43. doi.org/10.18273/revint.v43n2-2025003. e-print:arXiv:2412.20240 [math.GT].
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 (2023), No. 2, 103–123. 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
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].
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].
Fundamentals of cubic skein modules, with R. P. Bakshi, A. Christiana, H. Guo, D. Ibarra, L. Kauffman, S. Mukherjee, J. H. Przytycki, X. Wang. e-print:arXiv:2511.10959 [math.GT]
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.
