David Wright - Mathematical Publications

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The Mathematics & Music Course

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Some Recent Activities:

1. Polynomial Automorphism Groups, invited talk given at the meeting on Affine Geometry at Radboud University in Nijmegen, The Netherlands, October 26, 2007.

2. Survey on the Jacobian Conjecture, invited address given at the Conference on Affine Algebraic Geometry held at Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, January 7-13, 2007

3. Co-organizer of the International School and Workshop on Polynomial Automorphisms and Related Topics, held at the Institute of Mathematics, Hanoi, Vietnam, October 9-20, 2006, funded in part by the Abus Sadam International Centre for Theoretical Physisc, Trieste, Italy.

4. Co-organizer of the International School and Workshop on Polynomial Automorphisms and Related Topics, held at the Institute of Mathematics, Hanoi, Vietnam, October 9-20, 2006, funded in part by the Abus Sadam International Centre for Theoretical Physisc, Trieste, Italy.

5. Taught one-week mini-course on Polynomial Automorphism Groups at the Hanoi conferenced mentioned above. The Jacobian Conjecture as a problem in combinatorics, invited talk given at the Hanoi conference mentioned above.

6. Served on panel with H. Bass (Michigan) and S. Abhyankar (Purdue) fielding questions by members of the Vietnamese Mathematical Society on the role of mathematics in the 21st century, on October 18, 2006, in Hanoi, Vietnam.

7. The Jacobian Conjecture: a combinatorial approach, invited talk given December 16, 2005 at the joint meeting of the American Mathematical Society and the Taiwan Mathematical Society in Taichung, Taiwan.

Publications:

1. Algebras which resemble symmetric algebras, Proceedings of the Queens University Conference on Pure and Applied Algebra, Conference on Commutative Algebra, Kingston, Ontario, 1975.

2. Localization in the K-theory of invertible algebras, (with H. Bass), Journal of Pure and Applied Algebra 9 (1976), 89-105.

3. Locally polynomial algebras are symmetric algebras, (with H. Bass and E.H. Connell), Inventiones Mathematicae 38 (1977), 279-299.

4. Cancellation of variables of the form bt-a, Journal of Algebra 52, No. 1 (1978), 94-100.

5. The amalgamated free product structure of GL(k[X,Y]) and the weak Jacobian theorem for two variables, Journal of Pure and Applied Algebra 12 (1978), 235-251.

6. K(2,k[T,T-]) is generated by symbols (with R. Alperin), Journal of Algebra 59 (1979), 39-46.

7. Abelian subgroups of Autk[X,Y], and applications to actions on the affine plane, Illinois Journal of Mathematics 23, No. 4 (1979), 579-634.

8. A Mayer-Victoris sequence in the K-theory of algebras (with E. H. Connell), Journal of Pure and Applied Algebra 16 (1980), 149-165.

9. On the Jacobian conjecture, Illinois Journal of Mathematics 25, No. 3 (1981), 423-440.

10. The Jacobian conjecture: reduction of degree and formal expansion of the inverse, (with H. Bass and E.H. Connell), Bulletin of the American Mathematical Society 7, No. 2 (1982), 287-330.

11. Flat families of affine lines are affine-line bundles (with T. Kambayashi), Illinois Journal of Mathematics, 29, No. 3 (1985), 672-681.

12. Formal inverse expansion and the Jacobian conjecture, Journal of Pure and Applied Algebra 48 (1987), 199-219.

13. The tree formulas in the reversion of power series, Journal of Pure and Applied Algebra 57 (1989), 191-211.

14. Two dimensional Cremona groups acting on simplicial complexes, Transactions ot the American Mathematical Society 331, No.1 (1992), 281-300.

15. The Jacobian conjecture: Linear triangularization for cubics in dimension three, Linear and Multilinear Algebra 34 (1993), 85-97.

16. Normal forms and the Jacobian conjecture, Automorphisms of Affine Spaces (A. van den Essen, ed.), Kluwer Academic Publishers, The Netherlands, (1995), 145-156.

17. Reversion of power series and the extended Raney coefficients (with C. Chang, J. H. McKay, J. Towber, and S. Wang), Transactions of the American Mathematical Society 39, No. 5 (May, 1997), 1769-1782.

18. Affine surfaces fibered by affine lines over the projective line, Illinois Journal of Mathematics 41, No. 4 (Winter 1997), 589-605.

19. Reversion, Trees, and the Jacobian Conjecture, Contemporary Mathematics 264 (2000), 249-267.

20. Triangular factorizations of special polynomial automorphisms (with E. Hubbers), Journal of Algebra 235 (2001), 459-483 21.

21. D-Log and formal flow for analytic isomorphisms of n-space (with W. Zhao), Transactions of the American Mathematical Society 355, No. 8 (April 2003), 3117-3141

22. The Jacobian Conjecture: ideal membership questions and recent advances, Contemporary Mathematics 369 (2005), 261-276.

23. The Jacobian Conjecture as a problem in Combinatorics, in the monograph Affine Algebraic Geometry, in honor of Masayoshi Miyanishi,edited by Takayuki Hibi, published by Osaka University Press 2007

24. Polynomial automorphism groups, in the monograph Polynomial Automorphisms and Related Topics, Lecture Notes of the International School and Workshop ICPA2006, October 2006, Institute of Mathematics, Hanoi, Vietnam,edited by Hyman Bass, Nguyen Van Chau, and Stefan Maubach, published by Publishing House for Science and Technology, Hanoi, Vietnam, 2007

25. Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring, (with J. Berson and A. van den Essen), http://arxiv.org/pdf/0707.3151, submitted for publication.