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 solve problems in *mathematical biology*.

In my doctoral thesis, I established decomposition theorems for topological Azumaya algebras, and 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 Maria-Veronica Ciocanel.

### Publications

- Arcila-Maya N. (2023).
**Decomposition of symplectic vector bundles and topological Azumaya algebras with symplectic involution**. Preprint. arXiv. - Arcila-Maya N. (2022).
**Decomposition of topological Azumaya algebras with orthogonal involution.**Submitted. arXiv. - Arcila-Maya N., Bethea C., Opie M., Wickelgren K., Zakharevich I. (2022).
**Compactly Supported A¹-Euler Characteristic and the Hochschild Complex**,*Topology and its Applications*316. DOI. - Arcila-Maya, N. (2021).
**Decomposition of topological Azumaya algebras**.*Canadian Mathematical Bulletin,*1-19. DOI. - Arcila Maya N., Acosta Medina C., and Trujillo Casanova S. (2013).
**Numerical solution of a fractional differential equation Wave-Diffusion.**Revista NOOS, Vol. 2, 43 – 48, Universidad Nacional de Colombia, Manizales.

### Talks

- Apr 2022 – Invited speaker –
*Topological Azumaya algebras and the decomposition problem*– AMS 2023 Spring Central Sectional Meeting. - Aug 2022 – Invited speaker –
*Decomposition of Topological Azumaya Algebras in the Stable Range*– Algebraic Topology and Topological Data Analysis: A Conference in Honor of Gunnar Carlsson. - Jun 2021 – Invited speaker –
*Understanding topological Azumaya algebras with involution*(in Spanish) – I Encuentro de Estudiantes y Egresados de Matemáticas, Universidad Nacional de Colombia sede Manizales. - Dec 2020 – Invited speaker –
*Decomposition of topological Azumaya algebras with involution*– Homotopy Theory session in the 2020 CMS Winter Meeting. - Dec 2019 – Invited speaker –
*Decomposition of topological Azumaya algebras*– Topology session in the 2019 CMS Winter Meeting. - Mar 2019 –
*Integral cohomology of BPUn and the understanding of topological Azumaya algebras*– Women in Homotopy Theory and Algebraic Geometry II.

- Apr 2022 – Invited speaker – Decomposition Problem for Topological Azumaya Algebras with an Involution of the First Kind – Topology Seminar John Hopkins University and University of Virginia.
- Apr 2022 – Invited speaker –
*Álgebras Topológicas de Azumaya y el Problema de Descomposición*– SeTAGe Online seminar. - Apr 2022 – Invited speaker – Topological Azumaya Algebras and the Decomposition Problem – Homotopy Theory Seminar University of Pennsylvania.
- Apr 2022 – Invited speaker –
*Decomposition of Topological Azumaya Algebras in the Stable Range*– Peripatetic Seminar of the University of Calgary. - Mar 2022 –
*Decomposition of Topological Azumaya Algebras with Symplectic Involution*– Geometry & Topology Seminar, Duke University. - Oct 2020 – Invited speaker –
*Decomposition of topological Azumaya algebras*– Virtual topology seminar at the University of Illinois Urbana-Champaign.

### Workshops

- Jun 2023 – Participant – Rethinking Number Theory – Project: Representation of Codes Using Group Algebras by Henry Chimal-Dzul – Online
- Aug 2022 – Participant – VSU CBMS Conference on Topological Data Analysis and Persistence Theory – Valdosta State University.
- Jul 2021 – Participant – Motivic Homotopy: Interactions and Applications – IAS Park City Mathematics Institute.
- Ago 2020 – Invited participant – Cohomology of Finite Groups: Interactions and Aplications – Research Institute for Mathematics: MFO, Oberwolfach, Germany.
- Ago 2019 – Participant – Women in Topology III – Hausdorff Research Institute for Mathematics: HIM, Bonn, Germany.
- Nov 2017 – Participant – Workshop Women in Topology – MSRI, Berkeley, USA.

### Expository Writings

*The Steenrod algebra and its dual*.*Cohomology of Semidirect Products*. Master’s thesis on Adem-Ge-Pan-Petrosyan’s work on cohomology of crystallographic groups (in Spanish).