Research Interests

I am an applied topologist.  I study persistent homology and its abstractions.

Here is my cv and research statement.

Papers

R. MacPherson, A. Patel.  Persistent Sheaves.  In preparation.

J. Curry, A. Patel.  Classification of Constructible Cosheaves. arxiv.org/abs/1603.01587.

A. Patel.  Semicontinuity of Persistence Diagram. arxiv.org/abs/1601.03107.

F. Chazal, A. Patel, P. Skraba. Computing the Robustness of Roots. In the journal Applied Mathematics Letters, Volume 25, Issue 11, November 2012, Pages 1725 – 1728. 

H. Edelsbrunner, D. Morozov, A. Patel. Quantifying Transversality by Measuring the Robustness of Intersections. In the journal Foundations of Computational Mathematics, Volume 11, Issue 3, June 2011. 

H. Edelsbrunner, D. Morozov, A. Patel. The Stability of the Apparent Contour of an Orientable 2-Manifold. In Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications, eds. V. Pascucci, X. Tricoche, H. Hagen, and J. Tierny. Springer-Verlag, Heidelberg, Germany, 2011. 

Bendich, H. Edelsbrunner, M. Kerber, A. Patel. Persistent Homology Under Non-Uniform Error. In Proceedings of the 35th International Symposium on Mathematical Foundations of Computer Science, 2010, pp. 12-23. 

P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel. Robustness of Level Sets. In Proceedings of the 18th Annual European Symposium on Algorithms, 2010, 1–10. 

A. Patel. Reeb Spaces and the Robustness of Preimages, PhD thesis, Duke University, May 2010. 

H. Edelsbrunner, J. Harer, A. Patel. Reeb Spaces of Piecewise Linear Mappings. In Proceedings of the 24th Annual Symposium on Computational Geometry, 2008, 242-250. 

Education

Slides

Semicontinuity of Persistence Diagram - TGDA@OSU

The Quillen 2-Construction for Persistence - ATMCS6

Past Affiliations

Institute for Mathematics and its Applications (Fall 2013 - current)