University of Illinois at Urbana-Champaign

Sankar Dutta

Professor
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street (MC-382)
Urbana, Illinois 61801

Office: 331 Altgeld Hall
Phone: (217) 333-3168
Fax:  (217) 333-9576
e-mail: dutta@math.uiuc.edu

Mathematics Education

M.A., Calcuta University (Pure Mathematics), 1970

Research Assistant, Tata Institute of Fundamental Research, Bombay, India. 1971-75.

M.S., Ohio State University (Pure Mathematics), 1978

Ph.D., The University of Michigan, 1981.
Advisor: Prof. M. Hochster; Thesis Title: "Multiplicities over local rings"
Topic: Intersection Multiplicity on Local Rings.

Mathematics Positions

1981-86 Assistant Professor, University of Pennsylvania.
1983-84   Visiting Fellow, Institute for Advanced Study, Princeton.
1986 Assistant Professor, Department of Mathematics, University of Illinois.
1987 Post Doctoral Fellow, M.S.R.I., Berkeley (January-August).
1988 Associate Professor, Department of Mathematics, University of Illinois.
1993 Fellow, Danish Research Council (April-June).
1993 Visiting Professor-University of Utah (Fall).
1997 Professor, Department of Mathematics, University of Illinois.

Major Field in Mathematics:

Commutative Algebra

Research Area - Main Topics:

  1. Intersection Mulitplicity and related problems
  2. Canonical element conjecture and related problems
  3. Characteristic p ( > 0 ) techniques and its applications
  4. Several homological questions and conjectures

Teaching:

Undergraduate: Calculus in several variables, Linear Algebra
Graduate: Introductory level courses in commutative algebra and algebraic geometry
Topic Courses: 1. Local Cohomology
2. Smooth and Etale extensions
These two topics courses are offered at regular intervals.

Ph.D. Students:

Honors:

Publications:

  1. Multiplicities over local rings, Thesis, 1981, University of Michigan.
  2. Weak linking and Multiplicities, Journal of Pure and applied Algebra, Vol. 27, Number 2, February 1983, 111-130.
  3. Generalized Intersection Multiplicity of Modules, Trans. Amer. Math. Soc., Vol. 276, No. 2, April 1983, 657-669.
  4. Frobenius and multiplicities, Journal of Algebra, vol. 85, No. 2, December 1983, 424-448.
  5. Symbolic powers, intersection multiplicity and asymptotic behaviour of Tor, Journal of the London Math. Soc. (2) 28 (1983), 261-281.
  6. Generalized Intersection Multiplicities of Modules II, Proceeedings of AMS, Vol. 93, No. 2, February 1985, 203-204.
  7. (With M. Hochster & J. Mclaughlin) Modules of finite projective dimension with negative intersection multiplicities, Invent. Math. 79 (1985), 253-291.
  8. A note on a question of Bass, Trans. Amer. Math. Soc., Vol. 290, No 2, August 1985, 691-700.
  9. On the Canonical Element Conjecture, Trans. Amer. Math. Soc., Vol. 299, #2, Feb. 1987, 803-811.
  10. A Special Case of Positivity, Proceedings of the AMS, Volume 103, #2, June 1988, 344-346.
  11. Ext and Frobenius, Journal of Algebra, vol. 127, #1, Nov. 15, 1989, 163-177.
  12. Syzygies and Homological conjectures, Commutative Algebra, Hochster, Huneke, Sally Editors MSRI Publications, Springer-Verlag, 1989, 139-156.
  13. Modules of finite projective dimension with negative intersection multiplicities 11 (with M. Hochster and J. E. McLaughlin), preprint.
  14. A Note on Chow Groups and Intersection Multiplicity of Modules, The Journal of Algebra, Vol. 161, #1, October, 1993, 186-198.
  15. A Note on Chow Groups and Intersection Multiplicity of Modules 11, Journal of Algebra, Vol. 171, 370-382 (1995).
  16. On the Canonical Element Conjecture II, Math Zeit, Vol. 216, 379-388 (1994). [download pdf file]
  17. Dualizing Complex and the Canonical Element Conjecture, Journal of the London Math. Society, (2) 50 (1994) 477-487.
  18. A characterization of System of Parameters (with P. Roberts), Proc. of the AMS, Vol. 124, No. 3, March 1996, 671-675.
  19. Ext and Frobenius II, Journal of Algebra, vol. 186, 724-735 (1996). [download pdf file]
  20. The Canonical Element Conjecture--A brief survey and some new results, Commutative Algebra, Bruns. Herzog. Hochster. Vetter, International Conference, Vechta 1994, Vechtaer Universitiitschriften, 51-53.
  21. Dualizing Complex and the Canonical Element Conjecture II, Journal of the London Math Society, (2), 56(1997), 49-63. [download pdf file]
  22. A note on the Monomial Conjecture, Transactions of the AMS, vol. 350, #7, July 1998, p. 2871-2878. [download pdf file]
  23. A Theorem on Smoothness-Bass-Quillen, chow groups and Intersection Multiplicity of Serre, Transaction of the AMS, vol. 352, #4, 1635-1645. [download pdf file]
  24. A characterization of Gorenstein rings in characteristic p ( > 0 ), Proc. of the AMS, vol. 126, #6, June 1998, p. 1637-1643, 2000. [download pdf file]
  25. Splitting of Local Cohomology of Syzygies of the residue field, J. of Algebra, 244, 168-185 (2001). [download pdf file]
  26. On Modules of finite projective dimension over complete intersection, Proc. of the AMS, Vol. 131, No. 1, 2002, pp. 113-116. [download pdf file]
  27. On Negativity of Higher Euler Characteristics, American Journal of Mathematics, 126 (2004), 1341-1354. [download pdf file]
  28. Intersection Multiplicity of Modules in the Positive Characteristics, Journal of Algebra, 280 (2004), 394-411. [download pdf file]
  29. A Special Case of Positivity II, Proceedings of the AMS, Vol.133, No.7, 1891-1896, 2005. [download pdf file]
  30. On Efficient Generation of Pull-back of Tpn(-1), Illinois J. of Math, Vol. 51, No. 1, Spring 2007, 57-65. [download pdf file]
  31. Intersection multiplicity of Serre on regular schemes, J. of Algebra, No. 319, 2008, 1530-1554. [download pdf file]
  32. (With Phil Griffith), Intersection multiplicities, canonical element conjecture and the Syzygy problem, Michigan Math. J. 57 (2008), 227-247 [download pdf file]
  33. A connection between two sets of conjectures, The Mathematics Student, Special Centenary Volume (2007) pp. 71-80, Indian Mathematical Society. [download pdf file]
  34. Intersection Multiplicity on Blow-ups, Journal of Algebraic Geometry, 22 (2013), 85-103.[download pdf file]
  35. The monomial conjecture and order ideals, Journal of Algebra, 383 (2013), 232-241. [download pdf file]
  36. On a consequence of the order ideal conjecture, Journal of Pure and Applied Algebra, 219 (2015), 482-487. [download pdf file]
  37. On modules of finite projective dimension, Nagoya Math. Journal, 219 (2015), 87-111. [download pdf file]
  38. The monomial conjecture and order ideals II, Journal of Algebra, 454 (2016), 123-138. [download pdf file]
Last modified June 2, 2016