Published Articles
On the Khovanov Homology of T(2,n) Via Long Exact Sequence, inverse problems, geometric and topological aspects of representation theory, and low-dimensional topology, 83-94, Contemp. Math., 834, Amer. Math. Soc., Providence, RI, 2026. e-print:arXiv:2308.08452 [math.GT].
An unknotting robot, with C. Hui, D. Ibarra, L. Kauffman , E. McQuire, S. Mukherjee, C. Reid, 2024 MATRIX annals. Part I, 393-399, MATRIX Book Ser., 7, Springer, Cham, 2026.
On the notion of Khovanov A-adequacy, with L. Buchanan, H. Guo, M. Silvero, Y. Rong, 2024 MATRIX annals. Part I, 427-440, MATRIX Book Ser., 7, Springer, Cham, 2026. e-print: arXiv:2502.17637 [math.GT].
Exploring unimodality of the plucking polynomial with delay function, with D. Ibarra, A. Landry, J. H. Przytycki, Inverse problems, geometric and topological aspects of representation theory, and low-dimensional topology, 95-108, Contemp. Math., 834, Amer. Math. Soc., Providence, RI, 2026. e-print:arXiv:2311.18059 [math.GT].
Remarks on the Montesinos-Nakanishi 3-move conjecture, with R. P. Bakshi, B. Burton, H. Guo, D. Ibarra, S. Mukherjee, J. H. Przytycki, 2024 MATRIX annals. Part I, 401-410, MATRIX Book Ser., 7, Springer, Cham, 2026.
Indepence Complexes of Circle Graphs, with R. P. Bakshi, H. Guo, D. Ibarra, S. Mukherjee, M. Silvero, J. Spreer, 2024 MATRIX annals. Part I, 441-452, MATRIX Book Ser., 7, Springer, Cham, 2026. e-print:arXiv:2412.01125 [math.GT].
A robot that unknots knots, with C. Hui, D. Ibarra, L. Kauffman , E. McQuire, S. Mukherjee, C. Reid, J. Knot Theory Ramifications 35 (2026), no. 7, Paper No. 2650002, 38 pp. doi:10.1142/S0218216526500021. e-print:arXiv:2504.01254 [math.GT].
A Study of Gram Determinants in Knot Theory, with D. Ibarra, Algebraic structures in knot theory, 221--238, Contemp. Math., 827, Amer. Math. Soc., Providence, RI, 2025. e-print:arXiv:2402.09704 [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 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].
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.
