Seminar

 

Coordinates of Polynomial Algebras

 

Dr. Jie-Tai Yu

The University of Hong Kong

Abstract

Let K[x1 ,¼, xn] be the polynomial algebra of rank n over a field K of characteristic zero. A polynomial p in K[x1 ,¼, 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 ,¼, xn] if and only if there exist polynomials p2 ,…, pn, such that K[p, p2 ,¼, pn] = K[x1 ,¼, xn].

This talk will explore the close connection of the problem of recognizing coordinates of K[x1 ,¼, 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.

 

Date:

December 1, 2000 (Friday) 

Time:

4:00 - 5:00pm

Place:

Room 517, Meng Wah Complex

 

 

 

All are welcome