Publications:
1. The Amalgamated Product Structure of the Tame Automorphism Group in
Dimension Three, Transformation Groups, 20 (2015), 291304
http://arxiv.org/abs/1310.8325
2.
Stable Tameness of TwoDimensional Polynomial Automorphisms Over a
Regular Ring, (with J. Berson and A. van den Essen), Advances in
Mathematics 230 (2012), pp. 21762197
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,
21302134.
4. On the Image Conjecture (with A. van den Essen and W
Zhao), Journal of Algebra, 340 (2011), 211224.
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), 119.
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), 261276.
8.
DLog and formal flow for analytic isomorphisms of nspace (with W.
Zhao),
Transactions of the American Mathematical Society 355, No. 8 (2003),
31173141
9.
Triangular factorizations of special polynomial automorphisms (with E.
Hubbers), Journal of Algebra 235 (2001), 459483 21.
10.
Reversion, Trees, and the Jacobian Conjecture, Contemporary Mathematics
264 (2000), 249267.
11.
Affine surfaces fibered by affine lines over the projective line,
Illinois
Journal of Mathematics 41, No. 4 (1997), 589605.
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), 17691782.
13.
Normal forms and the Jacobian conjecture, Automorphisms of Affine
Spaces
(A. van den Essen, ed.), Kluwer Academic Publishers, The Netherlands,
(1995),
145156.
14.
The Jacobian conjecture: Linear triangularization for cubics in
dimension
three, Linear and Multilinear Algebra 34 (1993), 8597.
15.
Two dimensional Cremona groups acting on simplicial complexes,
Transactions
ot the American Mathematical Society 331, No.1 (1992), 281300.
16.
The tree formulas in the reversion of power series, Journal of Pure and
Applied Algebra 57 (1989), 191211.
17.
Formal inverse expansion and the Jacobian conjecture, Journal of Pure
and
Applied Algebra 48 (1987), 199219.
18.
Flat families of affine lines are affineline bundles (with T.
Kambayashi),
Illinois Journal of Mathematics, 29, No. 3 (1985), 672681.
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), 287330.
20.
On the Jacobian conjecture, Illinois Journal of Mathematics 25, No. 3
(1981),
423440.
21.
A MayerVictoris sequence in the Ktheory of algebras (with E. H.
Connell),
Journal of Pure and Applied Algebra 16 (1980), 149165.
22.
Abelian subgroups of Autk[X,Y], and applications to actions on the
affine
plane, Illinois Journal of Mathematics 23, No. 4 (1979), 579634.
23.
K(2,k[T,T]) is generated by symbols (with R. Alperin), Journal of
Algebra
59 (1979), 3946.
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),
235251.
25.
Cancellation of variables of the form bta, Journal of Algebra 52, No.
1 (1978), 94100.
26.
Locally polynomial algebras are symmetric algebras, (with H. Bass and
E.H.
Connell), Inventiones Mathematicae 38 (1977), 279299.
27.
Localization in the Ktheory of invertible algebras, (with H. Bass),
Journal
of Pure and Applied Algebra 9 (1976), 89105.
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 1116, 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 2125, 2014.
4. Automorphism Groups of Affine
nSpace, shrt course (foru lectures) at the Workshop on Affine Algebraic Geometry and the Jacobian Conjecture, Chern Institute for Mathematics, Nankai University, Tianjin
China, July 1519, 2014
5.
Amalgamations and Automorphism Groups, invited talk at the Kyoto
Workshop on Algebraic Varieties and Automorphism Groups, Kyoto
University, Kyoto, Japan, July 712, 2014
6. Amalgamations and Automorphism
Groups, invited talk at the Conference in honor of Hanspeter Kraft,
University of Basel, Basel, Swizerland, June 27, 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 1318, 2014.
8. Local criteria for stable tameness
of polynomial automorphisms, Special Session in Commutative Algebra,
AMS Central Section Meeting, Washington University, October 1820, 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 2327, 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 26, 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 2729, 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
1519, 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 610, 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 15, 2009.
28. Stable Tameness of TwoDimensional
Polynomial Automorphisms over a Regular Ring, invited address given at
the Conference on Algebraic Geometry, Bangalore, India, December 2228,
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 TwoDimensional
Polynomial Automorphisms, invited onehour 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 1719, 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 713,
2007
33.
Coorganizer of the International School and Workshop on Polynomial
Automorphisms and Related Topics, held at the Institute of Mathematics,
Hanoi, Vietnam, October 920, 2006, funded in part by the Abus Sadam
International Centre for Theoretical Physisc, Trieste, Italy.
34.
Coorganizer of the International School and Workshop on Polynomial
Automorphisms and Related Topics, held at the Institute of Mathematics,
Hanoi, Vietnam, October 920, 2006, funded in part by the Abus Sadam
International Centre for Theoretical Physisc, Trieste, Italy.
35.
Taught oneweek minicourse 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.

