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.

