Research Interests

My research focus lies at the intersection of algebraic topology, data analysis and computational methods. My main interest consists in the application and adaptation of ideas from algebraic and geometric topology to the study of high-dimensional and complex data. Other interests include computer vision and computational biology.

Selected Publications

• J. A. Perea, A Brief History of Persistence, Morfismos, vol. 23, no. 1, pp. 1-16, 2019.  Open
• J. A. Perea, Topological Time Series Analysis, Notices of the American Mathematical Society, vol. 66, no. 5, pp. 686-694, May 2019.  Open
• L. Polanco and J. A. Perea, Coordinatizing Data With Lens Spaces and Persistent Cohomology, to appear in Proceedings of the 31st Canadian Conference on Computational Geometry, 2019.  Open
• J. A. Perea, Sparse Circular Coordinates via Principal Z-bundles, to appear in Proceedings of the 15th Abel Symposium, 2019.  Open
• J. A. Perea, Multiscale Projective Coordinates via Persistent Cohomology of Sparse Filtrations, Discrete & Computational Geometry, vol. 59, no. 1, pp. 175-255, 2018.  Open
• J. A. Perea and J. Harer, Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis, Foundations of Computational Mathematics, vol. 15 no. 3, pp. 799-838, 2015.  Open
• J. A. Perea and G. Carlsson, A Klein-Bottle-Based Dictionary for Texture Representation, International Journal of Computer Vision, vol. 107 no. 1, pp. 75-97, 2014.  Open