Professor of Mathematics
| Department of Mathematics | |
|---|---|
| University of Oklahoma | |
| Norman, OK |
Krishnan.Shankar-1ou.edu
405 325 6711
About Me: the elevator pitch
I am a professor of mathematics at the University of Oklahoma; I have been here since 2002. I graduated from Reed College in Portland, Oregon with a B.A. and from the University of Maryland in College Park with a Ph.D (Mathematics). I did my thesis with Karsten Grove (now at Notre Dame). I am originally from India. Besides an abiding love of mathematics I am also keenly interested in educational technology and data science. My extra curricular interests include: yoga, swimming, stewardship of the environment and making and eating good food.
Research Interests
Riemannian Geometry, Lie groups, non-negatively curved manifolds.
Cryptography, analysis of algorithms.
Topological Data Analysis.
Spring 2018
Math 4743/5743: Introduction to Mathematical Statistics
This course is a sequel to the probability course I taught last fall. We will introduce rigorously the key concepts in statistics: random variables, hypothesis testing, analysis of variance, estimators, regression.
Math 6833: Topics in Geometry & Topology
This is the so-called "literacy course"; I will teach one unit of this (5 weeks: February 19th to March 31st). Proposed topic: Comparison theorems in Riemannian geometry i.e., Toponogov's theorem and its applications.
Recent Preprints
- Highly connected 7-manifolds and non-negative curvature (joint with Sebastian Goette and Martin Kerin), preprint. Article.
- Semi-free circle actions on 5-manifolds (joint with John Harvey and Martin Kerin), in preparation.
Papers
- On the fundamental groups of positively curved manifolds, Journal of Differential Geometry, 49 (1998) 179--182. Article.
- Rank two fundamental groups of positively curved manifolds (with Karsten Grove), Journal of Geometric Analysis, 10 (2000) 679--682. Article.
- Nilpotent numbers (with Jonathan Pakianathan), American Math. Monthly, 107 (2000), 631--634. Article.
- Isometry groups of homogeneous, positively curved manifolds, Differential Geometry & Appl., 14(1) (2001), 57--78. Article.
- On complexes equivalent to S^3 bundles over S^4 (with Nitu Kitchloo), Int. Math. Research Notices, 8 (2001), 381--394. Article.
- Strong inhomogeneity of Eschenburg spaces (with an Appendix written jointly with Mark Dickinson), Mich. Math. Journal, 50(1) (2002), 125--142. Article.
- The diffeomorphism type of the Berger space SO(5)/SO(3) (with Sebastian Goette and Nitu Kitchloo), American Journal of Mathematics, 126(2) (2004), 395--416. Article.
- Free isometric circle actions on compact, symmetric spaces (with Jost Eschenburg and Andreas Kollross), Geometriae Dedicata, 102 (2003), 35--44. Article.
- Non-negatively and positively curved metrics on circle bundles (with Kris Tapp and Wilderich Tuschmann), Proceedings of the AMS, 133(8) (2005), 2449--2459. Article.
- Spherical rank rigidity and Blaschke manifolds (with Ralf Spatzier and Burkhard Wilking), Duke Mathematical Journal, 1 (2005), 65--81. Article.
- On the cohomogeneity and symmetries of Eschenburg and Bazaikin spaces (with Karsten Grove and Wolfgang Ziller), Asian J. of Mathematics (S. S. Chern memorial volume), (2006), 647--662. Article.
- Snowflake groups, Perron-Frobenius eigenvalues and isoperimetric spectra (with Noel Brady, Martin Bridson and Max Forester), Geometry & Topology, 13 (2009), 141--187. Article.
- Conjugate points in length spaces (with Christina Sormani), Advances in Mathematics, 220(3) (2009), 791--830. Article.
- Riemannian submersions from simple, compact Lie groups (with
Martin Kerin), Muenster Journal of Mathematics, 5 (2012),
25--40. Article.
- Positively curved manifolds with large spherical rank (joint with Ben Schmidt and Ralf Spatzier), Commentarii Math. Helv., 19(2), (2016) 219--251. Article.
Other Preprints
- Square roots, continued fractions and the orbit of 1/0 in the hyperbolic plane (with Justin Roberts and Julian Rosen), 2006. Article.