S. Paul Smith's Curriculum Vitae

June 2000

Personal Information

• Name: Sholto Paul Smith
• Birthdate: 29 March, 1955
• Citizenship: New Zealand
• U.S. Resident Alien

Employment History
Systems Analyst, Datastream International, London	Mar. 1976-Oct. 1978
Assistant Professor, U.S.C., Los Angeles	Sep. 1981-Sep. 1983
SERC Research Assistant, University of Warwick, England	Oct. 1983-Aug. 1986
Assistant Professor, University of Washington	Sep. 1986-Sep. 1990
Associate Professor, University of Washington	Oct. 1990-Sep. 1993
Professor, University of Washington	Oct. 1993-present

Financial Awards and Research Grants

• University Junior National Scholarship, New Zealand, 1972-75
• Graduate Student Fellowship, University of Leeds, 1978-81
• British SERC Research Assistantship 1983-86
• Royal Society, UK-Israel Exchange Program, 1984

Research interests

Non-commutative algebra.
Enveloping algebras of Lie algebras, rings of differential operators on algebraic varieties, quantum groups, Noetherian rings, representation theory of Lie algebras, graded algebras (Sklyanin algebras), non-commutative algebraic geometry.

Professional Activities

• Editor
  • Algebras and Representation Theory.
  • Algebra and its Applications.
• Invited participant/speaker at the following meetings and conferences:
  • Enveloping Algebras, February 1982, Oberwolfach, (1 hour contributed talk).
  • Non-commutative Noetherian Rings, March 1983, Oberwolfach, (1 hour contributed talk).
  • Enveloping Algebras, July 1983, Durham (LMS), (2 hour invited talk).
  • Ring Theory, August 1983, Antwerp (NATO), (1 hour invited talk).
  • Geometry and Ring Theory, August 1984, Turkey (NATO) declined.
  • Enveloping Algebras, February 1985, Oberwolfach, (1 hour contributed talk).
  • Contact Franco-Belge en Algebre, April 1985, Antwerp, (1 hour invited talk).
  • D-Modules, June 1985, Oberwolfach, (1 hour contributed talk).
  • Non-commutative Noetherian Rings, April 1986, Oberwolfach, (1 hour contributed talk).
  • Ring Theory conference, June 1986, Leeds (LMS), (1 hour contributed talk).
  • Algebraic Groups, August 1986, Durham (LMS), declined.
  • Herstein Retirement conference, March 1987, Chicago.
  • Non-commutative Algebras, July 1987, Antwerp (NATO), declined.
  • Enveloping Algebras, August 1987, Oberwolfach.
  • Representation Theory and Non-commutative Algebras, December 1987,
  • Representation Theory at LSU, (1 hour invited talk).
  • Non-commutative Ring Theory, May 1988, Northern Illinois, DeKalb, (1 hour invited talk).
  • Amitsur Retirement conference, January 1989, Israel, (1 hour contributed talk).
  • Colloque en l'honneur de J. Dixmier, June 1989, Paris.
  • Noetherian Rings, June 1989, Oberwolfach, (1 hour contributed talk).
  • Non-commutative Rings, July 1989, MSRI, Berkeley, (3 one-hour invited talks).
  • Deformations of Algebras, June 1990, Amherst (AMS-IMS), (1 hour invited talk).
  • Developments in Algebra related to quantum groups, N. Carolina, Sept. 1991 (NSF), (1 hour invited talk).
  • Conference in Honour of M. Artin, Antwerp, May 1992, (1 hour invited talk).
  • Non-commutative Rings - new directions, Durham (LMS), July 1992 (3 hour invited talk).
  • Finite Dimensional Algebras, Aug. 1992, Canada, (1 hour invited talk, declined).
  • Noetherian Rings and Representation Theory, August 1993, Oberwolfach, (1 hour contributed talk).
  • Summer Algebra School, June 1994, Spain, (5 hour invited talk).
  • Representation Theory of Algebras, August 1994, Mexico, (2 hour invited talk).
  • European Algebra Meeting, February 1995, Edinburgh (2 hour invited talk, declined).
  • US-Belgium Science Days, May 1995, Belgium, (1 hour invited talk, declined).
  • Quantum groups and non-commutative geometry, May 1995, Italy, (2 hour invited talk, declined).
  • Welsh Mathematics Colloquium, May 1995, Wales (1 hour invited talk).
  • China-Japan Ring Theory Symposium, October 1995, Japan, (1 hour invited talk, declined).
  • Noetherian Rings and Representation Theory, August 1997, Oberwolfach, (1 hour contributed talk)
  • Representation Theory of Algebras, August 1998, Norway, (declined).
  • Homological Invariants in Representation Theory, March 1999, Greece, (declined).
  • Non-commutative Algebraic Geometry, July 1999, Max Planck Institut, Bonn (1 hour invited talk).
  • Quantum Groups, August 1999, Durham, England (declined).
  • Interactions between Non-commutative Algebra and Algebraic Geometry, February 2000, MSRI (1 hour invited talk).
  • American Mathematical Society Special Sessions (various).
  • British Mathematical Colloquium Special Sessions (various).
• Invited speaker at the following universities:
  UC San Diego, UC Los Angeles, UC Riverside, UC Santa Barbara, USC, Cincinatti, Duke, Utah, Oregon (Eugene), Texas (Austin), Penn State, UBC (Vancouver), Ottawa, Institut Henri Poincar\'e, Paris VI, Strasbourg, Antwerp, Nijmegen, London, Warwick, Leeds, Manchester, Edinburgh, Glasgow, Auckland (New Zealand), Christchurch (New Zealand), Weizmann Institute, Beersheva, Bar Ilan, Copenhagen, Universidad Nacional Autonoma de Mexico.
• Invited visitor at the following universities:
  • Manitoba, Canada, 1982 (invited by G. Krause) 4 weeks.
  • Limburgs, Belgium, 1984 (A. Ooms) 2 weeks.
  • Weizmann Institute, Israel, 1984 (A. Joseph) 6 weeks (supported by Royal Society).
  • Nijmegen, Holland, 1985 (A. van den Essen) 2 weeks.
  • Paris, France, 1985 (R. Rentschler) 3 weeks.
  • Paris, France, 1990 (R. Rentschler and A. Joseph) 2 weeks.
  • Univ. de Bretagne, France, 1990 (T. Levasseur) 2 weeks.
  • Weizmann Institute, Israel, 1990 (A. Joseph) 4 weeks (supported by US-Israel Binational Science Foundation).
  • M.I.T., 1991 (M. Artin) 1 week.
  • Antwerp, Belgium, 1991 (L. LeBruyn, M. van den Bergh) 3 weeks.
  • Beijing Normal University, 1995 to deliver 30 hours of lectures over 3 weeks.
  • Universidad Nacional Autonoma de Mexico, 1998, 2 weeks (R. Martinez-Villa).
  • Paris, France, 1998, 4 weeks (M.-P. Malliavin).
  • Copenhagen, Denmark, 1998, 2 weeks (P. Jorgensen).
  • Copenhagen, Denmark, 1999, 2 weeks (P. Jorgensen).
• Reviewer and/or referee for:
  • Algebras and Representation Theory, Journal of Algebra, Journal of Pure and Applied Algebra, Communications in Algebra, Pacific Journal of Mathematics, Glasgow Journal of Mathematics, Math. Zeitschrifte, Math. Annalen,
  • Journal, Bulletin, and Proceedings of the London Mathematical Society
  • Transactions, Proceedings, and Memoirs of the American Mathematical Society
  • Zentralblatt, Math Reviews
  • National Science Foundation, National Security Agency
  • Academic Press, Pitman Publishers (Research Notes in Mathematics), Cambridge University Press, Kluwer Academic Press, Marcel Dekker, Harper-Collins.
• Ph.D. students:
  • P. Perkins (1988), Differential Operators on Singular Curves
  • J. Staniszkis (1993), The Sklyanin Algebras
  • M. Vancliff (1993), Four-dimensional Regular Algebras
  • I. Mori (1998), Non-commutative Intersection Theory
  • A. Nyman (2001), Non-commutative Bundles

Publications

1. The Primitive Factor Rings of the Enveloping Algebra of sl(2,C), J. Lond. Math. Soc. 24 (1981) 97-108. (MR 82i:17016).
2. The Krull Dimension of the Enveloping Algebra of sl(2,C), J. Algebra 71 (1981) 189-194.
3. An Example of a ring Morita Equivalent to the Weyl Algebra A₁, J. Algebra 73 (1981) 552-555. (MR 83a: 16004).
4. Krull Dimension of factor rings of the enveloping algebra of a semi-simple Lie algebra, Proc. Camb. Phil. Soc. 93 (1983) 459-66. (MR 85a: 17007).
5. Central Localisation and Gelfand-Kirillov Dimension, Israel J. Math. 46 (1983) 33-39. (MR 85h: 16048).
6. Gelfand-Kirillov Dimension of rings of Formal Differential operators on Affine Varieties, Proc. Amer. Math. Soc. 90 (1984) 1-8. (MR 85d: 16019).
7. (with T. J. Hodges) Sheaves of non-commutative Algebras and the Beilinson-Bernstein equivalence of Categories, Proc. Amer. Math. Soc. 93 (1985) 379-388. (MR 86j: 17015).
8. (with T. J. Hodges) On the Global Dimension of Certain Primitive factors of the enveloping algebra of a semi-simple Lie Algebra, J. Lond. Math. Soc. 32 (1985) 411-418. (MR 87g: 17015).
9. (with T. J. Hodges) Differential Operators on the Flag Variety and the Conze embedding, submitted.
10. (with K. A. Brown) Bimodules over a solvable algebraic Lie algbera, Oxford Qu. J. Math., 36 (1985) 129-139. (MR 87d: 17009).
11. Differential Operators on the Affine and Projective Lines in positive characteristic, 1985 Seminaire d'Alg\`ebre M-P. Malliavin, Springer LNM 1220 (1986).
12. The Global Homological Dimension of the ring of Differential Operators on a non-singular variety over a field of Positive Characteristic, J. Algebra 107 (1987) 98-105.
13. Differential Operators on Commutative Algebras, Ring Theory Conference Proceedings (Antwerp 1985), Ed. F. M. J. van Oystaeyen, Springer-Verlag, LNM 1197 (1986). (MR 87m: 16030).
14. (with J. T. Stafford) Differential Operators on An Affine Curve, Proc. Lond. Math. Soc. 56 (1988) 229-259.
15. (with T. Levasseur) Primitive Ideals and Nilpotent Orbits in Type G₂, J. Algebra 114 (1988) 81-105.
16. (with R. Hart) Differential Operators on Some Singular Surfaces, Bull. Lond. Math. Soc. 19 (1987) 145-148. (MR 87m: 32027).
17. The simple D-module associated to the intersection homology complex for a class of plane curves, J. Pure and Applied Algebra 50 (1988) 287-294.
18. Curves, Differential Operators and finite Dimensional Algebras, 1986 S\'eminaire d'Alg\`ebre Malliavin, Springer LNM 1296 (1987) 158-176.
19. (with T. Levasseur, J. T. Stafford) The minimal nilpotent orbit, the Joseph ideal and differential operators, J. Algebra 116 (1988) 480-501.
20. A class of algebras like the enveloping algebra of sl(2,C), Trans. Amer. Math. Soc. 332 (1990) 285-314.
21. Overrings of primitive factor rings of U(sl(2,C)), J. Pure and Applied Alg. 63 (1990) 207-218.
22. Can the Weyl algebra be a fixed ring, Proc. Amer. Math. Soc., 107 (1989) 587-589.
23. Polynomial solutions to constant coefficient differential equations, Trans. Amer. Math. Soc., 329 (1992) 551-569.
24. (with M. S. Montgomery) U_q(sl(2,C)) and skew derivations, Israel J. Math., 72 (1990) 158-166.
25. Introduction to Quantum Groups for Ring Theorists, Proceedings of 1989 MSRI Conference on Non-commutative Noetherian Rings, Ed. L.W. Small, 1991, pp. 131-178.
26. (with J. T. Stafford) Regularity of 4-dimensional Sklyanin algebras, Compos. Math., 83 (1992) 259-289.
27. (with T. Levasseur) Modules over the 4-dimensional Sklyanin Algebra, Bull. Soc. Math. France, 121 (1993) 35-90.
28. (with J. Staniszkis) Irreducible representations of the 4-dimensional Sklyanin Algebra at points of infinite order, J. Algebra, 160 (1993) 57-86.
29. (with L. LeBruyn) Homogenized sl(2,C), Proc. Amer. Math. Soc., 118 (1993) 725-730.
30. (with L. LeBruyn and M. van den Bergh) Central Extensions of 3-dimensional Artin-Schelter regular algebras, Math. Zeit., 222 (1996) 171-212.
31. The 4-dimensional Sklyanin algebra at points of finite order, submitted.
32. Point modules over higher dimensional Sklyanin algebras, Math. Zeit., 215 (1994) 169-177.
33. The 4-dimensional Sklyanin Algebras, K-Theory, 8 (1994) 65-80.
34. (with J. Tate) The center of the 3-dimensional and 4-dimensional Sklyanin algebras, K-Theory, 8 (1994) 19-63.
35. Some finite dimensional algebras related to elliptic curves, in Representation Theory of algebras and related topics, CMS Conf. Proc., vol. 19, 315-348 (1996).
36. (with K. Ajitabh and J. Zhang) Auslander-Gorenstein rings, Comm. Alg., 26 (1998) 2159-2180.
37. (with K. Ajitabh and J. Zhang) Injective resolutions of some regular rings, Jour. Pure and Appl. Alg., 140 (1999) 1-21.
38. (with J. Zhang) Self-injective connected algebras, Comm. Alg., 25 (1997), no. 7, 2243-2248.
39. (with J. Zhang) A remark on Gelfand-Kirillov dimension, Proc. Amer. Math. Soc., 126 (1998), no. 2, 349-352.
40. (with J.Zhang) Curves on quasi-schemes, Algebras and Representation Theory, 1 (1998) 311-351.
41. (with I. Mori) Bezout's Theorem for quantum projective spaces, Jour. Pure and Appl. Alg., 157 (2001) 279-299.
42. (with I. Mori) The Grothendieck group of quantum projective space bundles, submitted.
43. (with J. Zhang) Fibers in Ore extensions, Algebr. Represent. Theory, 5 (2002) 411-431.
44. Subspaces of non-commutative spaces, Trans. Amer. Math. Soc., 354 (2002) 2131-2171.
45. Integral non-commutative spaces, J. Algebra, 246 (2002) 793-810.
46. Maps between non-commutative spaces, Trans. Amer. Math. Soc., to appear.
47. (with J. Zhang) Recognizing Modules over Dedkind domains, submitted.