Algebra Seminar


Tame and wild coordinates and automorphisms

of polynomial and free associative algebras


Mr. Shengjun Gong

The University of Hong Kong




Understanding automorphisms and coordinates are of the major topics in the study of problems concerning polynomial algebras, such as the Jacobian Conjecture, Zariski's Cancellation Problem, the Embedding Conjecture; also the Tame Generator Problem, which I will concentrate in the talk.

Firstly, I will give some results on tame and wild automorphisms of the polynomial algebra R[x,y] where R is a Q-algebra. We also consider the properties of the (tame or wild) coordinates, i.e., the images of x under the (tame or wild) automorphisms of R[x,y]. The case of the free associative algebra is treated as well.

Extending to three variables, I will introduce some results about the "tame generator problem", including the (strong) Nagata Conjecture and (strnog) Anick Conjecture recently solved by Dr. Yu and his colleagues. The emphasis lies in the methodologies such as: Peak reduction; Degree estimatation; Parametrization (for coordinates), and (in the free associative algebra case) Push-down to free metabelian algebras; Defining relations for tame subgroups of the automorphism groups.



June 29, 2006 (Thursday)


4:00 – 5:00pm


Room 517, Meng Wah Complex, HKU




All are welcome