Research | Niny Arcila-Maya

My research interests lie at the interface of algebra, algebraic geometry, and, algebraic topology. Also, I have been expanding my research interests to the area of topological data analysis and its application 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. I am currently working on the computation of the integral cohomology of classifying spaces of some projective spaces. I am also working on a TDA-MathBio project with Veronica Ciocanel.

Publications

2023

arXiv

Decomposition of symplectic vector bundles and Azumaya algebras

Niny Arcila-Maya

2023

arXiv Bib

@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

arXiv Bib

@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}
}

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

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

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

Numerical solution of a wave-diffusion fractional differential equation

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

Revista NOOS, 2013

Bib PDF

@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}
}