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:
- On values of linear and quadratic forms at
integral points, in: Number Theory (Ed. R.P. Bambah, V.C. Dumir,
Hindustan Book Agency and Indian National Science Academy, 2000.
- Affinely infinitely divisible distributions
and the embedding problem, (jointly with Klaus Schmidt),
Math. Res. Lett. 9 (2002), 607-620.
- Addendum to our paper ``Affinely
infinitely divisible distributions and the embedding problem'',
(jointly with Klaus Schmidt), Math. Res. Lett. 12 (2005),
- Anosov automorphisms on compact nilmanifolds
associated with graphs, (jointly with Meera Mainkar),
Trans. Amer. Math. Soc. 357 (2005), 2235-2251.
- 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
- Asymptotic behaviour under iterated random
linear transformations, (jointly
with Riddhi Shah), Math. Res. Lett. 11 (2004),467-480
- Dynamical properties of linear and projective
transformations and their applications, Indian J. Pure and Applied
Math., 35, 1365-1394 (2004).
- Locally compact groups with
dense orbits under $\Z^d$-actions by automorphisms, (jointly
with Nimish Shah and George Willis), Ergod. Th. Dynam. Syst. 26
- Convolution roots and embeddings of
probability measures on Lie groups, (jointly with M. McCrudden),
Adv. Math. (to appear).
- Invariant measures of the Euclidean
algorithm, (jointly with A. Nogueira),
Ergod. Th. Dynam. Syst. (to appear).
- Cumulative effect of random linear
transformations, (Preprint, 2005); this is an expository article
related to item 6 above.
- 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
- Simultaneous diophantine approximation with
quadratic and linear forms, J. Modern Dynamics 2 (2008), 129-138
(in the special issue dedicated to G.A. Margulis).
- 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
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.
- 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).
Vedic Maths' : facts and myths, published in
One India One People, Vol 4/6, January 2001, pp. 20-21.
- "Vedic Mathematics" : a dubious pursuit,
published in Newsletter of the Ramanujan Mathematical Society.
- 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.
- 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