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 a topologist. I am interested in persistent homology, Reeb spaces, stratified spaces, and bisheaves.

Here is my CV.

Graduate Students

Dustin Sauriol - MS Fall 2018

Alex McCleary - PhD expected Spring 2021

Alex Williams - PhD expected Spring 2023

Preprints

R. MacPherson and A. Patel. Persistent Local Systems. arXiv:1805.02539.

A. McCleary and A. Patel. Multiparameter Persistence Diagrams. arXiv:1905.13220.

A. Patel and D. Sauriol. Leray Spectral Sequence for Simplicial Maps. arXiv:1912.08288.

Published Papers

A. McCleary and A. Patel. Bottleneck Stability for Generalized Persistence Diagrams.
In the journal Proceedings of the AMS, Volume 148, Number 7, July 2020, pp 3149-3161.

J. Curry and A. Patel. Classification of Constructible Cosheaves.
In the journal Theory and Applications of Categories, Volume 35, 2020, Number 27, pp 1012-1047.

V. Nanda and A. Patel. Canonical Stratifications along Bisheaves.
In Proceedings of the Abel Symposium 2018: Topological Data Analysis, 2020.

A. Patel. Generalized Persistence Diagrams.
In the Journal of Applied and Computational Topology, May 2018
Slide talk: TGDA@OSU
Online talk: YouTube

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. [pdf]

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. [pdf]

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.

References

Allen Dudley Shepard. A Cellular Description of the Derived Category of a Stratified Space.
PhD Thesis, Brown University, 1985. [pdf]