Research | Niny Arcila-Maya

My research spans Algebraic Topology, and applications of Topological Data Analysis to other disciplines.

In my doctoral thesis, I established decomposition theorems for topological Azumaya algebras, and for topological Azumaya algebras with involutions of the first kind.

During my postdoc, I was a member of the Ciocanel Group, where I focused on understanding aster and ring structures in cellular actin filaments using TDA.

Publications

2026

arXiv

New results on difference distance magic labelings

Roza Aceska, Niny Arcila-Maya, Joshua Carlson, Alison Marr, Miriam Parnes, Kathleen Ryan, Houston Schuerger, and Jennifer F. Vasquez

2026

Submitted.

arXiv Bib

@misc{AAMCMPRSV2025,
  title = {New results on difference distance magic labelings},
  author = {Aceska, Roza and Arcila-Maya, Niny and Carlson, Joshua and Marr, Alison and Parnes, Miriam and Ryan, Kathleen and Schuerger, Houston and Vasquez, Jennifer F.},
  year = {2026},
  archiveprefix = {arXiv},
  primaryclass = {math.CO},
  note = {Submitted.}
}

2025

arXiv

Decomposition of symplectic vector bundles and Azumaya algebras

Niny Arcila-Maya

2025

Accepted for publication in the Journal of Homology, Homotopy and Applications.

arXiv Bib

@misc{TAAwS2025,
  title = {Decomposition of symplectic vector bundles and Azumaya algebras},
  author = {Arcila-Maya, Niny},
  year = {2025},
  archiveprefix = {arXiv},
  primaryclass = {math.AT},
  note = {Accepted for publication in the Journal of Homology, Homotopy and Applications.}
}

arXiv

Decomposition of topological Azumaya algebras with orthogonal involution

Niny Arcila-Maya

2025

Accepted for publication after corrections in the Journal of Pure and Applied Algebra.

arXiv Bib

@misc{TAAwO2025,
  title = {Decomposition of topological Azumaya algebras with orthogonal involution},
  author = {Arcila-Maya, Niny},
  year = {2025},
  archiveprefix = {arXiv},
  primaryclass = {math.AT},
  note = {Accepted for publication after corrections in the Journal of Pure and Applied Algebra.}
}

2022

Compactly supported A1-Euler characteristic and the Hochschild complex

Niny Arcila-Maya, Candace Bethea, Morgan Opie, Kirsten Wickelgren, and Inna Zakharevich

Topology and its Applications, 2022

Women in Topology III

DOI arXiv Bib HTML

@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}
}

CMB

Decomposition of topological Azumaya algebras

Niny Arcila-Maya

Canadian Mathematical Bulletin, 2022

DOI arXiv Bib HTML

@article{TAA2021,
  title = {Decomposition of topological Azumaya algebras},
  author = {Arcila-Maya, Niny},
  journal = {Canadian Mathematical Bulletin},
  volume = {65},
  number = {2},
  pages = {506--524},
  year = {2022},
  publisher = {Canadian Mathematical Society},
  doi = {10.4153/S000843952100045X}
}

2013

NOOS

Solución numérica de ecuaciones diferenciales fraccionarias de onda-difusión

Arcila Maya N., Acosta Medina C., and Trujillo Casanova S.

Revista NOOS, 2013

Undergraduate Research Project.

Bib PDF

@article{AMAMTC2013,
  title = {Soluci\'{o}n num\'{e}rica de ecuaciones diferenciales fraccionarias de onda-difusi\'{o}n},
  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, Sede Manizales},
  note = {Undergraduate Research Project.}
}