University of Puerto Rico    (787) 764 0000

    Professor Information

    Gabriel Montoya-Vega

    Address Department of Mathematics, 17 University Ave. Ste 1701
    San Juan PR, 00925-2537
    Office NCN II A-119
    Hours
    Actual Program
    Telephone (787) 764-0000 88274
    E-Mail ude.rpu@ayotnom.leirbag

    Education

    PhD, The George Washington University, 2022

    Research Interests

    Selected Publications

    1. G. Montoya-Vega, On the Khovanov Homology of T(2,n) Via Long Exact Sequence, AMS Contemp. Math., 834 (2026), Special Session on Inverse Problems, Geometric and Topological Aspects of Representation Theory, and Low-Dimensional Topology. Bookstore.ams.org. e-print:arXiv:2308.08452 [math.GT]. (2026)
    2. C. Hui, D. Ibarra, L. Kauffman, E. McQuire, G. Montoya-Vega, S. Mukherjee, C. Reid, A robot that unknots knots, Journal of Knot Theory and Its Ramifications. DOI 10.1142/S0218216526500021. e-print:arXiv:2504.01254 [math.GT]. (2025)
    3. A. Hernandez-Flores, G. Montoya-Vega, Alexander-Conway and bracket polynomials of a family of pretzel links, Rev. Integr. Temas Mat, 43 (2025), No. 2, 27–43. doi.org/10.18273/revint.v43n2-2025003. e-print:arXiv:2412.20240 [math.GT]. (2025)
    4. R. P. Bakshi, H. Guo, G. Montoya-Vega, S. Mukherjee, J. H. Przytycki, The Generalized Kauffman-Harary Conjecture is True, Algebraic & Geometric Topology 25 (2025) 2067–2081. DOI: 10.2140/agt.2025.25.2067. e-print:arXiv:2301.02645 [math.GT]. (2025)
    5. D. Ibarra, G. Montoya-Vega, A Study of Gram Determinants in Knot Theory, AMS Contemp. Math., 827 (2025), Special Session on Algebraic Structures in Knot Theory. Bookstore.ams.org. e-print:arXiv:2402.09704 [math.GT]. (2025)
    6. D. Ibarra, G. Montoya-Vega, A new Gram determinant from the Möbius band, Journal of Knot Theory and Its Ramifications, Vol. 33, No. 12, 2450037 (2024). doi:10.1142/S0218216524500378. e-print:arXiv:2304.05616 [math.GT]. (2024)
    7. G. Montoya-Vega, 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]. (2023)
    Book: Lectures in Knot Theory: An Exploration of Contemporary Topics, J. H. Przytycki, R. P. Bakshi, D. Ibarra, G. Montoya-Vega, D. Weeks, Springer Universitext, Springer International Publishing. 2024 March. DOI 10.1007/978-3-031-40044-5.

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