Gabriel Montoya-Vega

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I received my Ph.D. in Mathematics from The George Washington University in August 2022, under the supervision of Professor Józef H. Przytycki. From 2022 to 2025, I was an NSF-Ascend Postdoctoral Fellow at the CUNY Graduate Center in New York City, mentored by Professor Yongwu Rong.

My research interests lie in low-dimensional topology, particularly in knot theory. I study knot invariants such as Khovanov homology and Fox n-colorings, and investigate the structure of skein modules, their connections to framings of knots in 3-manifolds, and the role of Gram determinants in the algebraic and diagrammatic aspects of knot theory.

I am a co-author of the book: Lectures in Knot Theory: An Exploration of Contemporary Topics, published by Springer in 2024 and an alumnus of the Young Researchers at the Heidelberg Laureate Forum (2024).

In Fall 2025 I joined the math department at the University of Puerto Rico-Río Piedras.

Oberwolfach MFO - November 2021

While in GWU, I co-organized the Knots in Washington conference.

Together with Dionne Ibarra and Joan Licata, I co-organized the event Low Dimensional Topology: Invariants of Links, Homology Theories, and Complexity at the Matrix research institute in Australia in June 2024.

I am one of the local organizers of the Algebraic Structures in Topology conference taking place in San Juan, PR in July 2026.

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