Education

• M.Sc. Mathematics, Central College, Bangalore University (1985).
• Ph.D. Mathematics, Tata Institute of Fundamental Research, University of Bombay (1995).

Academic
Appoinments

• Research Associate, ISI, Bangalore (1995-97).
• Fellow, Chennai Mathematical Institute, Chennai (1997-2002).
• Reader, Chennai Mathematical Institute, Chennai (2002-2007).
• Reader, TIFR Centre for Applicable Mathematics, Bangalore (2007-2010).
• Associate Professor, TIFR Centre for Applicable Mathematics (since 2011).

Visiting Positions

• Visiting Mathematician, ICTP, Trieste (1991-92).
• Visiting Associate Professor, SUNY at Binghamton, USA (2000-2002).

Research Interests

• Broadly, my areas of interest are Riemannian Geometry, Ergodic Theory and Topology. I am particularly interested in the study of manifolds of nonpositive curvature and its geometric, dynamic and topological aspects.

Publications

RESEARCH ARTICLES
• Bounded geodesics and Hausdorff dimension
  Math. Proc. of the Camb. Phil. Soc. 116 (1994) 505-511.
• with F. T. Farrell:
  Rank 1 aspherical manifolds which do not support any nonpositively curved metric
  Comm. in Analysis and Geometry 2 (1994) 65-78.
• with E. Leuzinger:
  Bounded geodesics in rank-1 locally symmetric spaces
  Ergod. Th. & Dynam. Sys. 15 (1995) 813-820.
• with F. T. Farrell and S. K. Roushon:
  Knot complements and nonpositive curvature
  (Unpublished Preprint)
• with F. T. Farrell and S. K. Roushon:
  Surgery groups of knot and link complements
  Bull. London Math. Soc. 29 (1997) 400-406
• with F. T. Farrell and S. K. Roushon:
  Algebraic K-theory of pure braid groups
  Asian Journal of Mathematics, vol. 4 (2000) 337-344.
• with P. Sankaran:
  Orbits of certain endomorphisms of nilmanifolds and hausdorff dimension
  A Tribute to C. S. Seshadri: Perspectives in Geometry and Representation Theory (Eds: V. Lakshmibai et al.)
  Hindustan Book Agency, New Delhi, 2003, 124-132.
• with F. T. Farrell:
  Exotic negatively curved structures on Cayley hyperbolic manifolds
  Jour. Diff. Geom. 63 (2003) 41-62.
• with F. T. Farrell:
  Exotic structures and quaternionic hyperbolic manifolds
  Algebraic groups and Arithmetic, (Eds: S. G. Dani and G. Prasad)
  Narosa Publishing House, 2004.
• with F. T. Farrell:
  Nonpositivity: Curvature vs Curvature operator
  Proceedings of the American Mathematical Society, 133 (2005), 191-192.
• with S. Hersonsky and F. Paulin:
  Approximating points (Appendix to `On the almost sure spiraling of geodesics in negatively curved manifolds')
  Jour. Diff. Geom., 85 (2010) 271-314.
• with F. T. Farrell:
  Twisted doubles and Nonpositive curvature
  Bull. of Lond. Math. Soc., 41 (2009) 1053-1059

EXPOSITORY ARTICLES
• Riesz representation theorems
  Mathematics Newsletter, 15 (2005) 25-31.
• Continued fractions and Khinchine's theorem
  Mathematics Newsletter, 16 (2006) 1-5.
• The Kakeya needle problem
  Mathematics Newsletter, 16 (2006) 25-29.
• with Gowri Navada:

  On thin subsets of the real line

  Mathematics Newsletter, 17 (2007) 76-78.
• Classifying low-dimensional manifolds
  Mathematics Newsletter, 19 (2009) 10-15.
• Ricci flow and negative curvature
  Perspectives in Geometry and Topology, 11 (2010) 1-10.
• Curvature vs. Curvature Operator

  Special issue of the RMS Newsletter commemorating ICM 2010 in India, 19 (2010) 109-118.