Books :
Number theory and Combinatorics, Indian Academy of Sciences Masterclass series, 2017.
The congruence subgroup problem : an elementary approach aimed at
applications : TRIM Series, Vol. 24, 2003, Hindustan Book Agency, New Delhi,
India.
ISBN108185931380.
Distributed by the AMS except in India :
ISBN139788185931388.
Group theory : selected problems, Universities Press (India)
Private Ltd., 2004, Hyderabad, India.
Distributed by Orient Longman Pvt.Ltd.
ISBN 8173714916.
(www.universitiespress.com, www.orientlongman.com)
Hecke algebras, Intersection cohomology of Schubert varieties
and Representation theory (1984 vintage  unedited, unpublished !).
Some Lecture Notes, Talks, expository articles :
Lie, Witt and Leavitt algebras, June 19  July 3 2017.
Klassen Theorie, December 26, 2016 to January 7, 2017.
Factorization of domains and zerosum problems, July 2526, 2016.
The world of Diophantine equations, December 5, 2014.
Fifteen, two hundred and ninety and Bhargava, November 2014.
ISI Mathematics Day, outreach programme, November 29, 2014.
Support problem, Kummer theory, nested radicals  2nd talk, October 2014.
FLT  a very brief outline of ideas (in 1993).
Various decompositions in GL(n)  NBHM school on SL(2), TIFR Bombay (in 1992).
Matrices Elementary, My Dear Homs.
Mixed Motive, The Mathematical Intelligencer 1997.
Steinberg's chapters 6,7; ATM workshop on Chevalley groups, IISER Pune, May 2013.
What is the Tits index and how to work with it.
Ramanujan's mathematics  some glimpses.
HowlettLehrer theorem.
Ramanujan's route to roots of roots  RMS Mathematics Newsletter.
Group theory and tiling problems.
Talk in St.Petersburg Mathematical Society
Some applications of Chebotarev's density theorem
A modern Indian method
The ubiquitous modular group
Basic group theory.
Congruence subgroup problem.
Free Groups  Basics.
Some applications of representations of finite groups to
classical number theory.
Some exercises for the tutorials in the AIS above.
As easy as Pie I  At Right angles, April 2013.
As easy as Pie II  At Right angles, July 2013.
Groups  Beyond the undergraduate syllabi.
Lectures on commutative ring theory.
Very basic algebraic number theory
Hecke algebras, Intersection cohomology of Schubert varieties
and Representation theory (1984 vintage).
Primes and Riemann Hypothesis.
Algorithms in algebraic number theory.
Bringing the inner product out
Primes, cryptography and elliptic curves.
Is e^{sqrt{163}} odd or even ?
Existence and uniqueness of groups for root data.
Springer's chapter 16.
(with A.Raghuram) Groups acting on trees.
More grouptheoretic applications of geometric methods.
Explicit reciprocity laws.
Introduction to Number fields, Proc. Conference on cyclotomic fields, Bhaskaracharya
Pratishthana, Poona, 1999.
Absolute values and completions in brief.
(with D.S.Nagaraj) A quick introduction to algebraic geometry and elliptic curves.
Elliptic curves over finite fields.
(with D.S.Nagaraj) MordellWeil theorem.
Subgroup growth.
Some studentprojects supervised :
Linear Programming and game theory.
Theory of noncommutative rings and representation theory.
Dirichlet's class number formula and Brun's theorem.
Theory of block designs.
Classification of surfaces.
Finite groups of integer matrices.
Basics of Galois theory and applications.
Beginnings of Polya's theory.
A converse to the CayleyHamilton theorem.
Necklaces, periodic points and permutation representations.
How safe is Sam Lloyd's bet ?
A numbertheoretic game.
The AmitsurLevitzkii identity via graph theory.
Weyl's equidistribution theorem.
Sums of powers of primitive roots.
Theorema Aureum  I.
Theorema Aureum  II.
The support problem.
What is Hilbert's 17th problem?
Division rings and their theory of equations.
