S.G. Dani's homepage

Welcome to my homepage!

To begin with, here is some basic information about me:

My contact information

My list of papers

Here are some of my recent papers available in soft copy:
  1. On values of linear and quadratic forms at integral points, in: Number Theory (Ed. R.P. Bambah, V.C. Dumir, R.J. Hans-Gill), Hindustan Book Agency and Indian National Science Academy, 2000.
  2. Affinely infinitely divisible distributions and the embedding problem, (jointly with Klaus Schmidt), Math. Res. Lett. 9 (2002), 607-620.
  3. Addendum to our paper ``Affinely infinitely divisible distributions and the embedding problem'', (jointly with Klaus Schmidt), Math. Res. Lett. 12 (2005), 817-820.
  4. Anosov automorphisms on compact nilmanifolds associated with graphs, (jointly with Meera Mainkar), Trans. Amer. Math. Soc. 357 (2005), 2235-2251.
  5. Asymptotic behaviour of measures under automorphisms in Probability Measures on Groups: Recent Directions and Trends (Proceedings of CIMPA-TIFR School, Mumbai 2002), Narosa Publishing House, New Delhi, (international distribution by the American Mathematical Society), 2006; pp. 149-178
  6. Asymptotic behaviour under iterated random linear transformations, (jointly with Riddhi Shah), Math. Res. Lett. 11 (2004),467-480
  7. Dynamical properties of linear and projective transformations and their applications, Indian J. Pure and Applied Math., 35, 1365-1394 (2004).
  8. Locally compact groups with dense orbits under $\Z^d$-actions by automorphisms, (jointly with Nimish Shah and George Willis), Ergod. Th. Dynam. Syst. 26 (2006)), 1443-1465
  9. Convolution roots and embeddings of probability measures on Lie groups, (jointly with M. McCrudden), Adv. Math. (to appear).
  10. Invariant measures of the Euclidean algorithm, (jointly with A. Nogueira), Ergod. Th. Dynam. Syst. (to appear).
  11. Cumulative effect of random linear transformations, (Preprint, 2005); this is an expository article related to item 6 above.
  12. Diophantine approximation and dynamics of unipotent flows on homogeneous spaces, Pure and Applied Math. Quarterly 4 (2008), 147-166; this is an article on the work of G.A. Margulis.
  13. Simultaneous diophantine approximation with quadratic and linear forms, J. Modern Dynamics 2 (2008), 129-138 (in the special issue dedicated to G.A. Margulis).
  14. Factors, roots and embeddings of measures on Lie groups, an expanded text version of a talk given at the conference "Perspectives in Mathematical Sciences" held at ISI Bangalore, 4-8 February 2008.

    Here is a general article; it is the text version of a "Hardikar Memorial" talk given at the S.P. College, Pune on 25 August 2007.

    Fine structure of the number line

    I have also been interested in mathematics of the ancient times, especially from India. I have given some talks on the subject. The following article on the topic was published in Current Science in 2003:

    On the Pythagorean triples in the Sulvasutras

    In the nineties I got interested in debunking the so called "Vedic mathematics". Here are some of my articles on the topic; the first is a detailed article; the others are short; the last two are recent.

    1. Myth and reality : on 'Vedic Mathematics' ; an updated version of a two-part article in Frontline (Vol 10, No. 21, October 22, 1993, pp. 90-92 and Vol 10, No. 22, November 5, 1993, pp. 91-93).
    2. Vedic Maths' : facts and myths, published in One India One People, Vol 4/6, January 2001, pp. 20-21.
    3. "Vedic Mathematics" : a dubious pursuit, published in Newsletter of the Ramanujan Mathematical Society.
    4. Vedic Maths: myths and reality ; based on a presentation made at the second national conference on "Technology & Innovations in Mathematics Education" (TIME), from December 1-4, 2007.
    5. Vedic Mathematics in Perspective, ; text version of a talk given at the XXXI Session of the Indian Social Science Congress, at SNDT University, Mumbai, on 29 December 2007.

    I wrote also an article on Prof. M.S. Raghunathan, which was published in Frontline in January 2001, the text of which may be found here:

    Professor M.S. Raghunathan

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