Date & Time: Wednesday, July 13, 2016, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: Avinash Sathaye,
Univ. of Kentucky, Lexington
Title: Sub-principle Planes
Abstract: An affine domain $A$ over a field $k$ is called a sub-principle plane if it satisfies the following: \begin{itemize} \item $A=k[p,q]\subset k[u,v]$ where $k[u,v]$ is a polynomial ring in two variables over $k$. \item There is a polynomial $g\in k[u,v]$ such that $k[p,q,g] = k[x,y]$. \end{itemize} We will discuss the problem of identifying properties of $p,q$ which ensure the condition of $A$ being a sub-principle plane. The problem is clearly important in order to determine if the polynomial $F(X,Y,Z)$ defining the kernel of the homomorphism $k[X,Y,Z]\rightarrow k[u,v]$ is an abstract plane. A detailed description of $A$ is hoped to help with the solution of the three dimensional epimorphism problem.