Jonathan Treviño-Marroquín
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.
Since Fall 2022, I am co-organizing the Grad Student's Seminar at CIMAT joint with Carlos Espinosa-Valdéz, Daniel Posadas, Edgar Castañeda, Julio Barrera, Lorena Noh, Pedro Ramírez-Moreno and Rocío Ríos.
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.
Preprints:
(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
(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
(Oct, 2022.) Semi-coarse Spaces. Joint with Antonio Rieser. arXiv:2210.02569
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.
Teaching assistant:
(Fall 2022.) Topology I. Universidad de Guanajuato.
