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. ISBN-10-81-85931-38-0. Distributed by the AMS except in India : ISBN-13-978-81-85931-38-8.
  • Group theory : selected problems, Universities Press (India) Private Ltd., 2004, Hyderabad, India. Distributed by Orient Longman Pvt.Ltd. ISBN 81-7371-491-6. (www.universitiespress.com, www.orientlongman.com)
  • Hecke algebras, Intersection cohomology of Schubert varieties and Representation theory (1984 vintage - unedited, unpublished !).


  • Articles published in Resonance



    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 zero-sum problems, July 25-26, 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.
  • Howlett-Lehrer 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 group-theoretic 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) Mordell-Weil theorem.
  • Subgroup growth.


    Some student-projects 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 Cayley-Hamilton theorem.
  • Necklaces, periodic points and permutation representations.
  • How safe is Sam Lloyd's bet ?
  • A number-theoretic game.
  • The Amitsur-Levitzkii 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.