\documentclass[11pt]{article}
\usepackage[letterpaper, left=1in, top=1in, bottom=1in, right=1in]{geometry}
\usepackage{verbatim}
\setlength{\parindent}{0in}
\pagestyle{empty}
\begin{document}
\vspace{\fill}
\begin{center}\LARGE
\textsc{}
\par
\textsc{Colloquium}
\end{center}
\vspace{\fill}
\begin{center}\LARGE
\textit{Approximation results for varieties of low degree}
\end{center}
\vspace{\fill}
\begin{center}\Large
Brendan Hassett\par
Rice University
\end{center}
\vspace{\fill}
\textbf{Abstract:} In the 1930's, C.C. Tsen showed that a homogeneous polynomial over the
function field of a complex projective curve has a nontrivial solution
provided the degree of the polynomial is less than than the number of
variables.  In 2001 Graber, Harris, and Starr generalized this result by
proving that every rationally connected variety over the function  
field of a curve has a rational point.  We can recast this in geometric terms:   
If $f \!:X \to B$ is surjective map from a smooth projective variety to a curve
with rationally connected fibers, then $f$ admits a section.  Once we know
that a section exists, we can ask approximation questions about the
sections:  Can we find a section through a prescribed set of points?   
With prescribed Taylor series at those points?  Our results depend on the
singularities occuring in the fibers of $f$.    (joint with Y.  
Tschinkel)\vspace{\fill}
\begin{center}\Large
Thursday, March 6, 2008, 4:00 pm\par
Mathematics and Science Center: W201
\end{center}
\vspace{\fill}
\begin{center}\Large
Refreshments will be served in the Department Lounge at 3:30PM
\end{center}
\vspace{\fill}
\begin{center}\LARGE
\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
\end{center}
\end{document}