headshot

Amit Patel

Assistant Professor
Department of Mathematics
Colorado State University

Email
akpatel@colostate.edu

Office
Weber 217

Address
Department of Mathematics
1874 Campus Delivery
Fort Collins, CO 80523-1874

Research Interests

I am an applied topologist. Much of my work is motivated by questions coming from data analysis. What is the shape of a data set? Data is noisy so any answer to this question must be stable to perturbations. Most of my work has focused on two tools: persistent homology and Reeb spaces for maps (a.k.a. stratified coverings).

I have been working on developing a theory of persistence for maps since graduate school. This problem is very hard. I have made progress towards this direction by studying something we call the "well groups" associated to a map. For the past five years, Bob MacPherson and I have been working on a sheaf theoretic approach to this question. Expect a paper soon!

I am looking for graduate students interested in thinking about data analysis, topology, (co)sheaves, and algorithms.

Here is my CV.

Teaching Spring 2017

Math 567 - Abstract Algebra II

Papers

J. Curry and A. Patel. Classification of Constructible Cosheaves. Preprint.

A. Patel. Generalized Persistence Diagrams. Preprint.
Slide talk: TGDA@OSU

V. de Silva, E. Munch, A. Patel. Categorified Reeb Graphs.
In the journal Discrete & Computational Geometry, June 2016, Volume 55, Issue 4, pp 854-906.

P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel. Homology and Robustness of Level and Interlevel Sets.
In the journal Homology, Homotopy, and Applications; Volume 15; Number 1; 2013; pp 51-72.

F. Chazal, A. Patel, P. Skraba. Computing the Robustness of Roots.
In the journal Applied Mathematics Letters, Volume 25, Issue 11, November 2012, pp 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.
Part of the series Mathematics and Visualization.

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, pp 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, pp 242-250.