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% beamerstructure2 presentation
\documentclass{beamer}
\usetheme{Warsaw}
\setbeamertemplate{navigation symbols}{}
\title{Sectionally complemented chopped lattices}
\author{George Gr\"atzer\inst{1}
\and Harry Lakser\inst{1}
\and Michael Roddy\inst{2}}
\institute{\inst{1} University of Manitoba
\and \inst{2} Brandon University}
\date{Conference on Lattice Theory, 2006}
%Note that multiple authors are separated by \verb+\and+ and so are
%the various institutions. The \verb+\date+ command is treated as a
%footnote.
\begin{document}
\begin{frame}
\titlepage
\end{frame}
%To show an outline of the whole presentation, we have to fake it.
%The command \verb+\tableofcontents+ provides you with the Table of
%Contents of the whole presentation only if there are no parts.
%With an optional argument, it can also provide the Table of Contents
%of a specific part: \verb+\tableofcontents[part=3]+ is the
%Table of Contents of Part 3. We also use the \ttt{pausesections}
%option.
%The Table of Contents of the whole presentation is given in an
%unnumbered section and three unnumbered subsections.
\section*{Outline}
\subsection*{Part I: Background}
\begin{frame}
\frametitle{Outline of Part I: Background}
\tableofcontents [part=1,pausesections]
\end{frame}
\subsection*{Part II: Characterizing the 1960 sectional complement}
\begin{frame}
\frametitle{Outline of Part II: Characterizing the\\1960 sectional complement}
\tableofcontents[part=2,pausesections]
\end{frame}
\subsection*{Part III: The general problem}
\begin{frame}
\frametitle{Outline of Part III: The general problem}
\tableofcontents[part=3,pausesections]
\end{frame}
%Now come the three parts. Each part is introduced with two frames:
%the first with \verb+\partpage+ (which is the ``titlepage'' for the
%part) and the second with the command \verb+\tableofcontents+
%(for the part).
%We provide each section with a frame to activate it.
\part{Background}
\begin{frame}
\partpage
\end{frame}
\begin{frame}
\frametitle{Part I\\Outline}
\tableofcontents
\end{frame}
\section{Chopped lattices}
\begin{frame}
\frametitle{Defining chopped lattices}
Starting the definitions
\end{frame}
\section{Ideals and congruences}
\begin{frame}
\frametitle{Ideals}
Continuing the definitions
\end{frame}
\part{Characterizing the 1960 sectional complement}
\begin{frame}
\partpage
\end{frame}
\begin{frame}
\frametitle{Part II\\Outline}
\tableofcontents
\end{frame}
\section{What it is not}
\begin{frame}
\frametitle{Not maximal, minimal, or fixed point}
Counterexamples
\end{frame}
\section{The characterization theorem}
\begin{frame}
\frametitle{The main result}
State the characterization theorem
\end{frame}
\part{The general problem}
\begin{frame}
\partpage
\end{frame}
\begin{frame}
\frametitle{Part III\\Outline}
\tableofcontents
\end{frame}
\section{The Lakser Theorem}
\begin{frame}
\frametitle{The problem}
Stating the general problem and Harry's observation
\end{frame}
\section{A small counterexample}
\begin{frame}
\frametitle{Four-element overlap}
Counterexample
\end{frame}
\section{A cyclic counterexample}
\begin{frame}
\frametitle{Three cycle}
Cyclic counterexample
\end{frame}
\end{document}
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