Some special cases of the Abhyankar-Sathaye Conjecture

Prof. Neena Gupta(ISI, Kolkata) will deliver a talk at Bhaskaracharya Pratishthana, Pune.

Day & Date: Sunday 26th March 2023
Timing: 5:00 PM
Venue: AV Hall, Bhaskaracharya Pratishthana, Pune.

Thus begins a poem composed by Shreeram S. Abhyankar in 1970.
Polynomials are introduced at a very early stage in our studies. Yet there are many interesting fundamental problems on polynomial rings which are easy to state but difficult to approach.One such problem is the famous Abhyankar-Sathaye Conjecture which asserts that in characteristic zero, any affine hyperplane in a polynomial ring is a coordinate.An affine line is a coordinate in characteristic zero. This is the well-known Epimorphism Theorem proved by Abhyankar-Moh and Suzuki independently around 1975

However, the next case, the affine plane case, is still open in general. Some special cases have been considered by Sathaye, Russell, Wright, Kaliman and other mathematicians.In this talk we shall mention known results on epimorphism theorems over rings due to Bhatwadekar and his school. We shall also see some partial generalisations of the results of Sathaye and Russell on linear planes to higher dimensions.

All are cordially invited to attend the talk.