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I am a Ph.D. student in the Applied Geometry and Topology research group at the Centro de Investigación en Matemáticas [CIMAT] in Guanajuato under the direction of Antonio Rieser. I am working on developing homotopy theory for Limit and Čech Closure spaces and applications to Topological Data Analysis [TDA].
I am also interested in coarse geometry. In my Master's thesis; also under the direction of Antonio Rieser, I explored Semi-Coarse Spaces, a variation of Coarse Spaces. We defined an interesting notion of homotopy in that category and constructed a natural Vietoris-Rips homology that is invariant with respect to this homotopy.
I am working as a part-time professor at Universidad Autónoma de Nuevo León [UANL], where I am giving initial courses of basic math to under-graduated students. Here, I am co-organizing a Student Seminar joint with Gerardo Hernández, Gerardo Palafox and a group of undergrad students: Renata Capistran, Praxedis Jimenez, Román Montemayor, and Mariangel Sanchez.
About me:
I am from Monterrey, a big city in northeastern Mexico. I started my academic life as an electro-mechanical engineering student, but halfway my studies I decided to become a Math student. While completing my Math degree, I was also a Teaching Assistant at the engineering faculty for a period of two years, during which time I had the opportunity to meet people who encouraged me to continue with my studies as a graduate student at CIMAT.
Papers:
(Feb, 2025.) Semi-coarse Spaces. Joint with Antonio Rieser. arXiv:2210.02569
(Oct, 2023.) A Second Homotopy Group for Digital Images. Joint with Gregory Lupton, Oleg Musin, Nicholas A. Scoville, and P. Christopher Steacker. arXiv:2310.08706
Preprints:
(Oct, 2025) Rational Homotopy in Pseudotopological spaces. arXiv:2510.18282
(May, 2024) Graphs and Their Vietoris-Rips Complexes Have the Same Pseudotopological Weak Homotopy Type. arXiv:2406:00149
(Apr, 2024) Semi-coarse Spaces: Fundamental Groupoid and the van Kampen Theorem. arXiv:2404.08874
(Mar, 2024) Universal Coverings for Limit and Pseudotopological Spaces. arXiv:2403.18852
Most Recent Talks:
(May, 2024.) An Introduction to Digital Topology (Spanish). Primer Ciclo de Conferencias 2024 del Posgrado en Ingeniería en Sistemas [V]
(Jan, 2024.) An Introduction to Semi-coarse Spaces. GEOTOP-A International Conference
(Oct, 2023.) Buscando n-esferas en la Homotopía Digital (Spanish). 56vo Congreso Nacional de la Sociedad Mexicana de Matemáticas
(Sept, 2023.) Homotopy in Semi-coarse Spaces. Iberoamerican and Pan Pacific International Conference on Topology and its Applications
(Jun, 2023.) Cubriendo sin vecindades (Spanish). Cuarto Encuetro Nacional de Estudiantes de Posgrado en Matemáticas
Most Recent Posters:
(Nov, 2023.) Cyclic Graphs in Semi-coarse Spaces. 9th Mexican Workshop of Applied Geometry and Topolgy [P]
Events:
(May, 2023.) CMO-BIRS Interactions between Algebraic Topology and Geometric Group Theory.
(Mar, 2023.) AIM Workshop on Discrete and Combinatorial Homotopy Theory.
Part-time professor:
(Fall 2025) Linear Algebra (Bachelor). Universidad Autónoma de Nuevo León
(Fall 2025) Logic and Sets (Bachelor). Universidad Autónoma de Nuevo León
(Fall 2025) Theory of Fields and Rings (Bachelor). Universidad Autónoma de Nuevo León
(Fall 2025) Topology (Bachelor). Universidad Autónoma de Nuevo León
Teaching assistant:
(Fall 2022.) Topology I. Universidad de Guanajuato
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