C S Aravinda

C. S. Aravinda

TIFR Centre for Applicable Mathematics
P O Box 6503, Sharadanagara
G K V K Post, BANGALORE - 560 065.

aravinda -AT- math.tifrbng.res.in


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


  • 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.


  • 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    (Unpublished Preprint)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

  • 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.