Books and Edited Volumes

  1. (coedited with Hema Srinivasan and J. K. Verma), Commutative Algebra and Algebraic Geometry, Contemporary Mathematics Vol. 390, American Mathematical Society, Providence, 2005, xiv+173 pp.
        Review from MathSciNet   Review from Zentralblatt 

  2. (with B. V. Limaye) A Course in Calculus and Real Analysis , Undergraduate Texts in Mathematics, Springer, New York, 2006, x+432 pp..  
    [Click on the title to view the authors' Website of this book containing useful information and updates; Click here to view the publisher's page of the book.]
        Review from MathSciNet   Review from Zentralblatt 

  3. (with B. V. Limaye) A Course in Multivariable Calculus and Analysis , Undergraduate Texts in Mathematics, Springer, New York, 2010, xii+475 pp.
    [Click on the title to view the authors' Website of this book containing useful information and updates; Click here to view the publisher's page of the book.]
        Review from MathSciNet   Review from Zentralblatt 

  4. (coedited with A. R. Shastri, M. K. Srinivasan and J. K. Verma), Combinatorial Topology and Algebra, RMS Lecture Notes Series Vol. 18, Ramanujan Mathematical Society, Mysore, 2013, xiv+208 pp.
        Review from MathSciNet   Review from Zentralblatt 

  5. (coedited with A. Sathaye), Special issue of the Journal of Algebra and Its Applications in honor of Shreeram S. Abhyankar, Vol. 14, No. 9 (2015); 14 Articles, 281 pp.
        Contents   Foreword (PDF)  

Papers (in reverse chronological order)

        [Many of these papers, and sometimes new ones not listed here, are also available on the arXiv.]

  1. (with Peter Beelen and Mrinmoy Datta) Maximum number of common zeros of homogeneous polynomias over finite fields, Proceedings of the American Mathematical Society, to appear; arXiv:1705.10185 [math.AG], 2017.
        Abstract & Contents   PDF  

  2. (with Prasant Singh) Minimum distance and the minimum weight codewords of Schubert codes, Finite Fields and their Applications, Vol. 49 (2018), pp. 1-28.
        Abstract & Contents   PDF  

  3. (with Yves Aubry, Wouter Castryck, Gilles Lachaud, Michael E. O'Sullivan, and Samrith Ram) Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory, Algebraic Geometry for Coding Theory and Cryptography (IPAM, Los Angeles, CA, February 2016), E. Howe, K. Lauter and J. Walker Eds., Association for Women in Mathematics Series, Vol. 9, Springer, New York, 2017, 37 pp.
        Abstract & Contents   PDF  

  4. (with Mrinmoy Datta) Remarks on Tsfasman-Boguslavsky conjecture and higher weights of projective Reed-Muller codes,
    Arithmetic, Geometry, Cryptography and Coding Theory (Luminy, France, May 2015), A. Bassa, A. Couvreur and D. Kohel Eds., Contemporary Mathematics, Vol. 686, American Mathematical Society, Providence, RI, 2017, pp. 157--169.
        Abstract & Contents   Review from Zentralblatt  PDF  

  5. (with Mrinmoy Datta) Number of solutions of systems of homogeneous polynomial equations over finite fields, Proceedings of the American Mathematical Society, Vol. 145, No. 2 (2017), pp. 525-541.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF  

  6. (with Mrinmoy Datta) On a conjecture of Tsfasman and an inequality of Serre for the number of points on hypersurfaces over finite fields, Dedicated to M. A. Tsfasman and S. Vlăduţ on their 60th birthdays, Moscow Mathematical Journal, Vol. 15, No. 4 (2015), pp. 715-725.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF  

  7. (with C. Krattenthaler) Computation of the a-invariant of ladder determinantal rings, Dedicated to the memory of S. Abhyankar, Journal of Algebra and Its Applications, Vol. 14, No. 9. (2015), Article 1540014, 24 pp.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF  

  8. (with Peter Beelen and Sartaj Ul Hasan) Linear codes associated to determinantal varieties, Discrete Mathematics, Vol. 338 (2015), 1493-1500.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF  

  9. (with Mrinmoy Datta) Higher weights of affine Grassmann codes and their duals, Algorithmic Arithmetic, Geometry, and Coding Theory (Luminy, France, June 2013), S. Ballet, M. Perret, and A. Zaytsev Eds., Contemporary Mathematics, Vol. 637, American Mathematical Society, Providence, RI, 2015, pp. 79-91.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF  

  10. (with B. Jonov and B.A. Sethuraman) Hilbert series of certain jet schemes of determinantal varieties, Pacific Journal of Mathematics, Vol. 272, No. 1 (2014), pp. 147-175.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF  

  11. (with Krishna Kaipa) Automorphism groups of Grassmann codes, Finite Fields and Their Applications, Vol. 23 (2013), pp. 80-102.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  12. (with Samrith Ram) Arithmetic progressions in a unique factorization domain, Acta Arithmetica, Vol. 54, No. 2 (2012), pp. 161-171.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  13. (with Samrith Ram) Enumeration of splitting subspaces over finite fields, Arithmetic, Geometry, Cryptography and Coding Theory, (Luminy, France, March 2011 ), Y. Aubry, C. Ritzenthaler, and A. Zykin Eds., Contemporary Mathematics, Vol. 574, American Mathematical Society, Providence, RI, 2012, pp. 49-58.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  14. (with Peter Beelen and Tom Høholdt) Duals of affine Grassmann codes and their relatives, IEEE Transactions on Information Theory, Vol. 58, No. 6 (2012), pp. 3843-3855.
        Abstract & Contents   Review from MathSciNet   PDF   PS   DVI

  15. (with Samrith Ram) Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields, Finite Fields and Their Applications, Vol. 17, No. 5 (2011), pp. 461-472.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  16. (with Mario Garcia-Armas and Samrith Ram) Relatively prime polynomials and nonsingular Hankel matrices over finite fields, Journal of Combinatorial Theory, Series A, Vol. 118, No. 3 (2011), pp. 819-828.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  17. (with Sartaj Ul Hasan and Meena Kumari) Primitive polynomials, Singer cycles, and word-oriented linear feedback shift registers, Designs, Codes and Cryptography, Vol. 58, No. 2 (2011), pp. 123-134.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  18. (with Peter Beelen and Tom Høholdt) Affine Grassmann codes, IEEE Transactions on Information Theory, Vol. 56, No. 7 (2010), pp. 3166-3176.
        Abstract & Contents   Review from MathSciNet   PDF   PS   DVI

  19. (with G. Lachaud) Corrigenda and Addenda: Étale Cohomology, Lefschetz theorems and number of points of singular varieties over finite fields, Moscow Mathematical Journal, Vol. 9, No. 2 (2009), pp. 431-438.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF  

  20. (with A. R. Patil and H. K. Pillai) Subclose families, threshold graphs, and the weight hierarchy of Grassmann and Schubert codes, in: Arithmetic, Geometry, Cryptography and Coding Theory (Luminy, France, Nov 2007), G. Lachaud, C. Ritzenthaler, and M. Tsfasman Eds., Contemporary Mathematics, Vol. 487, American Mathematical Society, Providence, RI, 2009, pp. 87-99.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  21. (with B. V. Limaye) A geometric approach to saddle points of surfaces, The Australian Mathematical Society Gazette, Vol. 36 (2009), No. 2, pp. 127-136.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  22. (with A. R. Patil and H. K. Pillai) Decomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes, Finite Fields and their Applications, Vol. 15, No. 1 (2009), pp. 54-68.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  23. (with B. V. Limaye) Sylvester's minorant criterion, Lagrange-Beltrami identity, and nonnegative definitenes, The Mathematics Student 2007, Special Centenary Volume (2008), pp. 123--130.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  24. (with K. N. Raghavan) Hilbert functions of points on Schubert varieties in the Symplectic Grassmannian, Transactions of the American Mathematical Society, Vol. 358, No. 12 (2006), pp. 5401-5423.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  25. (with M. A. Tsfasman) Schubert varieties, linear codes and enumerative combinatorics, Finite Fields and their Applications, Vol. 11, No. 4 (2005), pp. 684-699.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  26. (with C. Krattenthaler) The Hilbert series of Pfaffian rings, in: Algebra, Arithmetic and Geometry with Applications (West Lafayette, 2000), C. Christensen, C. Bajaj, G. Sundaram and A. Sathaye Eds., Springer-Verlag, New York (2004), pp. 337-356.
        Abstract, Contents & Afternotes   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  27. (with M. A. Tsfasman) Classical varieties, codes and combinatorics, in: Formal Power Series and Algebraic Combinatorics, (Vadstena, 2003) Actes/Proceedings, K. Eriksson and S. Linusson Eds., Linköping University, Sweden (2003), pp. 75-84.
        Abstract & Contents   PDF   PS   DVI

  28. (with G. Lachaud) Étale Cohomology, Lefschetz theorems and number of points of singular varieties over finite fields, Dedicated to Yuri I. Manin on the occasion of his 65th birthday, Moscow Mathematical Journal, Vol. 2, No. 3 (2002), pp. 589-631.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  29. Hilbert functions of ladder determinantal varieties, Discrete Mathematics, Vol. 246 (2002), pp. 131-175.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI  

  30. (with G. Lachaud) Number of solutions of equations over finite fields, and a conjecture of Lang and Weil, in: Number Theory and Discrete Mathematics (Chandigarh, 2000), A. K. Agarwal, B. Berndt, C. Krattenthaler, G. L. Mullen, K Ramachandra and M. Waldschmidt Eds., Trends in Mathematics, Birkhäuser, Basel (2002), pp. 269-291.[Published in India by Hindustan Book Agency, New Delhi, 2002.]
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt  PDF   PS   DVI

  31. (with G. Lachaud) Hyperplane sections of Grassmannians and the number of MDS linear codes, Finite Fields and their Applications, Vol. 7, No. 4 (2001), pp. 468-506.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt   PDF   PS   DVI

  32. A note on Hodge's postulation formula for Schubert varieties, in: Geometric and Combinatorial Aspects of Commutative Algebra (Messina, 1999), J. Herzog and G. Restuccia Eds., Lecture Notes in Pure and Applied Mathematics, Vol. 217, Marcel Dekker, New York (2001), pp. 211-220.
        Abstract & Contents   Review from MathSciNet   Review from Zentralblatt   PDF   PS   DVI  

  33. (with G. Lachaud) Higher weights of Grassmann codes, in: Coding Theory, Cryptography and Related Areas (Guanajuato, 1998), J. Buchmann, T. Hoeholdt, H. Stichtenoth and H. Tapia-Recillas Eds., Springer-Verlag, Berlin (2000), pp. 122-131.
        Abstract, Contents & Afternotes   Review from MathSciNet   Review from Zentralblatt   PDF   PS   DVI  

  34. On the enumeration of indexed monomials and the computation of Hilbert functions of ladder determinantal varieties, in: Formal Power Series and Algebraic Combinatorics, (Barcelona, 1999) Actes/Proceedings, C. Martinez, M. Noy and O. Serra Eds., Universitat Politecnica de Catalunya, Spain (1999), pp. 225-232.
        Abstract   PDF   PS   DVI

  35. Young bitableaux, lattice paths and Hilbert functions, Journal of Statistical Planning and Inference (Special issue on Lattice Path Combinatorics and Applications), Vol. 54 (1996), pp. 55-66.
        Abstract   Review from MathSciNet   Review from Zentralblatt   PDF   PS

  36. Young multitableaux and higher dimensional determinants, Advances in Mathematics, Vol. 121, No. 2 (1996), pp. 167-195.
        Review from MathSciNet   Review from Zentralblatt   PDF   PS

  37. (with G. Lachaud) Grassmannians over finite fields and MDS Codes, Proceedings of the Discussion Meeting on Cryptography and Computation, (Coordinators: C. E. Veni Madhavan and R. Balasubramanian), Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, 1995, 4 pages.
        PDF   PS  

  38. Abhyankar's work on Young tableaux and some recent developments, in: Algebraic Geometry and its Applications (West Lafayette, IN, 1990), C. Bajaj Ed., Springer-Verlag, New York, (1994), pp. 233-265.
        Review from MathSciNet   Review from Zentralblatt   PDF   PS

  39. (with S. S. Abhyankar) Young tableaux and linear independence of standard monomials in multiminors of a multimatrix, Discrete Mathematics,, Vol 96 (1991), pp. 1-32.
        Review from MathSciNet   Review from Zentralblatt   PDF

  40. (with M. V. Deshpande) Algebraic characterization of compact abelian groups, American Mathematical Monthly, Vol. 98, No. 3 (1991), pp. 235-237.
        Review from MathSciNet   PDF   PS

Obituary and Foreword

  1. Remembering Shreeram S. Abhyankar, (with appendices by A. Sathaye, B. Singh, S. D. Cutkosky, and R. V. Gurjar),
    Asia Pacific Mathematics Newsletter, Vol. 3, No. 1 (2013), pp. 22-30.
    [This article is also reprinted, with permission from the APMN, in Resonance Vol. 18, No. 5 (2013), pp. 397-411, and the
    RMS Mathematics Newsletter, Vol. 23 , No. 4 (2013), pp. 271-279. ]
        PDF (APMN)   PDF (Resonance)   PDF (RMS-ML)  

  2. (with A. Sathaye), Foreword to the Special Issue in Honor of Shreeram S. Abhyankar, Journal of Algebra and its Applications,
    Vol. 14, No. 9 (2015), Article 1502001, 4 pp.
        PDF  

Expository Articles

  1. Discriminants in Algebra and Arithmetic, Bona Mathematica, Vol. 11, No. 2-3 (2000), pp. 43-62. [This article is also reprinted in the Bulletin of the Bombay Mathematical Colloquium, Vol. 15, No. 1-2 (1999*), pp. 33-47 with permission from the Editor of Bona Mathematica. *: date of actual publication: Jan 2001.]
        Abstract & Contents   PDF   PS   DVI  

Articles on Pedagogy

  1. Teaching Calculus using Internet: Some Experiments and Experiences, in: Science, Technology and Mathematics Education for Human Development, Proceedings of the CASTME-UNESCO-HBCSE International Conference (Goa, Feb. 2001), Vol. 1, Eds., S. C. Agarkar and V. D. Lale , Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai, 2002, pp. 219-223.
        [Article as a PDF file]   [Article in HTML format]   [Article as a MS Word File]
    Related News Item:   Tribune India (July 2001),

  2. Effective Teaching and Modern Perspectives in Mathematics, Souvenir of the Mathematics Association, IIT Bombay, 2002, pp. 37-42.
    [This article is a slightly revised version of the text of an invited talk at the CEP Course on Effective Teaching for Technical Teachers, Department of Humanities and Social Sciences, IIT Bombay, January 1996.]
        [Article as a PDF file]   [Article as a PS file]

Lecture Notes

  See here.

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