2. Stable Tameness of Two-Dimensional Polynomial Automorphisms Over a Regular Ring, (with J. Berson and A. van den Essen), Advances in Mathematics 230 (2012), pp. 2176-2197 http://arxiv.org/pdf/0707.3151.

3. Images of Locally Finite Derivations of Polynomial Algebras in Two Variables (with A. van den Essen and W Zhao), Journal of Pure and Applied Algebra 215 (2011), no 9, 2130-2134.

4. On the Image Conjecture (with A. van den Essen and W Zhao), Journal of Algebra, 340 (2011), 211-224.

5. Polynomial automorphism groups, Chapter 1 of 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), 1-19.

6. 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

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

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

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

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

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

12. 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 (1997), 1769-1782.

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

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

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

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

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

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

19. 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.

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

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

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

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

24. 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.

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

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

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

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

Book:

1.  Mathematics and Music, Mathematical World, Volume 28, American Mathematical Society, Providence, RI, 2009

Some Recent Scholarly Activities:

1. Representative for the American Mathematical Society at the Committee on Education meeting at the Annual Meeting of the American Association for the Advancement of Science (AAAS), San Jose, CA, February 11-16, 2015.

2. Amalgamations and Automorphism Groups, colloquium talk at Wayne State University, Detroit Michigan, November 17, 2014.

3. Amalgamations and Automorphism Groups, invited talk at the International Conference on Affine Algebraic Geometry and the Jacobian Conjecture, Chern Institute for Mathematics, Nankai University, Tianjin China, July 21-25, 2014.

4. Automorphism Groups of Affine n-Space, shrt course (foru lectures) at the Workshop on Affine Algebraic Geometry and the Jacobian Conjecture, Chern Institute for Mathematics, Nankai University, Tianjin China, July 15-19, 2014

5. Amalgamations and Automorphism Groups, invited talk at the Kyoto Workshop on Algebraic Varieties and Automorphism Groups, Kyoto University, Kyoto, Japan, July 7-12, 2014

6. Amalgamations and Automorphism Groups, invited talk at the Conference in honor of Hanspeter Kraft, University of Basel, Basel, Swizerland, June 2-7, 2014

7. Representative for the American Mathematical Society at the Committee on Education meeting at the Annual Meeting of the American Association for the Advancement of Science (AAAS), Chicago, IL, February 13-18, 2014.

8. Local criteria for stable tameness of polynomial automorphisms, Special Session in Commutative Algebra, AMS Central Section Meeting, Washington University, October 18-20, 2013.

9. Panelist, How to Prepare for Graduate School in Mathematics, Field of Dreams Conference sponsored but The National Alliance for Doctoral Studies in the Mathematical Sciences, Phoenix, AZ, October 2, 2013.

10. Mathematics and Music, Colloquiium Lecture to Student Body, Emory and Henry College, October 1, 2013.

11.  Panelist, Roundtable on Music and Mathematics (part of the Initiative for Mathematics and the Arts sponsored by Institute for Mathematical Sciences, Madrid), Residencia de Estudiantes, Madrid, Spain, September 26, 2013.

12.  Mathematics and Music, Colloquium lecture, Institute for Mathematical Sciences, Madrid, Spain, September 24, 2013.

13. Mathematics and Music, invited talk at the New Piasa Chautauqua, Elsah, Il. July 15, 2013.

14. Mathematics and Music, Math Week Lecture, Utah Valley University, March 29, 2013.

15. Survey on Polynomial Automorphism Groups, invited presentation at the conference on Groups of Automorphisms in Birational and Affine Geometry, Centro Internazionale per la Ricerca Matematica (CIRM), Trento, Italy, October 29 - November 3, 2012

16. Amalgamations and Automorphism Groups, invited presentation at the Conference in Birational and Affine Geometry, Steklov Institute, Moscow, Russia, April 23-27, 2012.

17. Mathematics and Music, keynote address at the Missouri Section Meeting of the Mathematical Association of America, University of Missouri, St Louis April 13, 2012

18. The Amalgamated Product Structure of the Tame Automorphism Group in Dimension Three, invited talk at the Conference in Honor of Professor Mohan Kumar, Kerala School of Mathematics, Kozikode, India, April 2-6, 2012

19. Mathematics and Music, colloquium talk at Portland State University, Portland, OR, November 4, 2011.

20. Polynomial Automorphisms and the Jacobian Conjecture, Seminar talk at Portland State University, Portland, OR, November 4, 2011.

21.  Chaired the annual meeting of the AMS Committee on Education, October 27-29, 2011.

22. Mathematics and Music, a presentation given at the National Council of Teachers in Mathematics (NCTM) meeting in St. Louis, MO, October 26, 2011.

23. Appointed Chair of the American Mathematical Society's Committee on Education.  Appointment made by AMS President Geoarge Andrews on November 8, 2010.

24. New conjectures related to the Jacobian Conjecture, colloquium talk at the Indian Statistical Institute, Kolkata, India, August 16, 2010.  This occurred during an invited visit to ISI August 15-19, 2010, during which I gave daily lectures on locally polynomial algebras and stable tameness.

25. Represented the American Mathematical Society at the annual meeting of the Canadian Mathematical Society, Frederikton, NB, June 3, 2010.

26. Commutator Formulas for Polynomial Automorphisms, invited address at the Workshop on Automorphisms of Affine Spaces at Radboud University in Nijmegen, The Netherlands, July 6-10, 2009.

27. Commutator Formulas for Polynomial Automorphisms, invited address at Affine Algebraic Geometry, a conference in honour of Peter Russell, McGill University, Montreal, Quebec, Canada, June 1-5, 2009.

28. Stable Tameness of Two-Dimensional Polynomial Automorphisms over a Regular Ring, invited address given at the Conference on Algebraic Geometry, Bangalore, India, December 22-28, 2008.

29. Elected in a national election to the Council of the American Mathematical Society in November 2008; attended my first Council meeting in Chicago, IL, April 18, 2009.

30. A New Result on Stable Tameness of Two-Dimensional Polynomial Automorphisms, invited one-hour lecture at the Special Session in Affine Algebraic Geometry at the sectional meeting of the American Mathematical Society held at Western Michigan University, Kalamazoo, Michigan, October 17-19, 2008.

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

32. 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

33. 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.

34. 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.

35. 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.

36. 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.

37. 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.