Coordinates of Polynomial Algebras


Dr. Jie-Tai Yu

The University of Hong Kong


Let K[x1 ,, xn] be the polynomial algebra of rank n over a field K of characteristic zero. A polynomial p in K[x1 ,, xn] is called a coordinate polynomial (or for short, a coordinate) if p is an automorphic image of x1. In otherwords, p is a coordinate of K[x1 ,, xn] if and only if there exist polynomials p2 ,, pn, such that K[p, p2 ,, pn] = K[x1 ,, xn].

This talk will explore the close connection of the problem of recognizing coordinates of K[x1 ,, xn] and following open problems in commutative algebra and affine algebraic geometry:

1. Jacobian problem of Keller;

2. Tame generator problem of Cohn and Nagata;

3. Embedding problem of Abhyankar and Sathay;

4. Concellation problem of Zariski;

5. Injective problem (Campbell, Shpilrain and Yu);

6. Stably tame coordinates problem (Shpilrain and Yu).

Recent progress by the speaker and his colleagues on above problems approached by means of coordinate polynomials will also be reported.



December 1, 2000 (Friday) 


4:00 - 5:00pm


Room 517, Meng Wah Complex




All are welcome