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).
