Professor of Mathematics

Department of Mathematics | |
---|---|

University of Oklahoma | |

Norman, OK |

Krishnan.Shankar-1ou.edu

405 325 6711

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.

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.

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.

*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.

*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.

*Square roots, continued fractions and the orbit of 1/0 in the hyperbolic plane*(with Justin Roberts and Julian Rosen), 2006. Article.