I am interested in most things persistent homology, applied topology, and topology. My last two-three years have focused on building a theory of persistence for stratified mappings to manifolds. This involves stratification theory, intersection theory, 2-categories, and lax sheaves.
I'm looking for a tenure track position starting in Fall 2015. Here is my cv.
R. MacPherson , A. Patel. Persistent Sheaves. In preparation.
V. de Silva, E. Munch, A. Patel. Categorified Reeb Graphs. In preparation.
P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel. Homology and Robustness of Level and Interlevel Sets. In the journal Homology Homotopy Appl., Volume 15, Number 1, 2013, Pages 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, 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.
Doctor of Philosophy, Duke University, May 2010, Advisor: Herbert Edelsbrunner
Master of Science, University of Illinois at Urbana-Champaign, May 2003, Advisor: Jeff Erickson
Bachelor of Science, University of Illinois at Urbana-Champaign, May 2001
Institute for Mathematics and its Applications (Fall 2013 - current)