| Polynomial rings are very simple but interesting objects with many challenging open problems. In this talk, I will discuss some problems on polynomial rings which I have studied. The problems I will treat are Hilbert's 14th Problem which asks finite generation of certain subalgebras of a polynomial ring, and the Tame Generators Problem on a generating set for the automorphism group of a polynomial ring. If time allows, I will also mention a problem on "initial algebras" which are subalgebra analogues to initial ideals in Groebner basis theory.
|