**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.