My research spans Algebraic Topology, Topological Data Analysis and its application to other disciplines, and, more recently, the Scholarship of Teaching and Learning.
In my doctoral thesis, I established decomposition theorems for topological Azumaya algebras, and for topological Azumaya algebras with involutions of the first kind.
Publications
2023
arXiv
Decomposition of symplectic vector bundles and Azumaya algebras
@misc{TAAwS2023,title={Decomposition of symplectic vector bundles and Azumaya algebras},author={Arcila-Maya, Niny},year={2023},eprint={2311.17029},archiveprefix={arXiv},primaryclass={math.AT}}
2022
arXiv
Decomposition of topological Azumaya algebras with orthogonal involution
Niny Arcila-Maya
2022
Accepted for publication after corrections at the Journal of Pure and Applied Algebra
@misc{TAAwO2022,title={Decomposition of topological Azumaya algebras with orthogonal involution},author={Arcila-Maya, Niny},year={2022},eprint={2212.06720},archiveprefix={arXiv},primaryclass={math.AT},note={Accepted for publication after corrections at the Journal of Pure and Applied Algebra}}
TA
Compactly supported A1-Euler characteristic and the Hochschild complex
Niny Arcila-Maya, Candace Bethea, Morgan Opie, Kirsten Wickelgren, and Inna Zakharevich
@article{ABOWZ2022,title={Compactly supported A1-Euler characteristic and the Hochschild complex},author={Arcila-Maya, Niny and Bethea, Candace and Opie, Morgan and Wickelgren, Kirsten and Zakharevich, Inna},journal={Topology and its Applications},volume={316},number={2},pages={108108},year={2022},publisher={Canadian Mathematical Society},doi={https://doi.org/10.1016/j.topol.2022.108108},note={Women in Topology III}}
@article{AMAMTC2013,title={Numerical solution of a wave-diffusion fractional differential equation},author={N., Arcila Maya and C., Acosta Medina and S., Trujillo Casanova},journal={Revista NOOS},volume={2},pages={43–48},year={2013},publisher={Universidad Nacional de Colombia, Manizales}}