[Tex/LaTex] line 66: Missing number, treated as zero \end{frame}

beamer

\documentclass{beamer}

\usepackage[latin1]{inputenc}

\usetheme{Warsaw}
\usepackage[english]{babel}
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{array}
\usepackage{graphicx}
\usepackage{multirow}
\usepackage[font=scriptsize,format=plain,justification=centering,labelformat=empty]{caption}
\usepackage{textcomp}
\usepackage{animate}

\title[Bose-Einstein Condensates and Superfluidity]{Bose-Einstein Condensates and Superfluidity}
\author{Pablo Ramos and Alessandro Genova}
\institute{Rutgers University}
\date{December 17, 2013}
\begin{document}

\begin{frame}
\titlepage
\end{frame}

\begin{frame}
\frametitle{Table of Contents}
\tableofcontents 
\end{frame}

\section{Introduction}

 \begin{frame}
  \frametitle{What is a Bose-Einstein Condensate ($BEC$)}
  \begin{columns}
  \begin{column}{0.6\textwidth}
    \begin{enumerate}
      \item Collection of bosons (particles integer spin) at temperatures near to 0 \ \textdegree K
      \item If the system is describe by $n_i=\frac{g_i}{e^{(\epsilon_i-\mu)/kT}+1}$
         \begin{itemize}
      \item Particles collapse $\Rightarrow$ Lowest quantum state
      \item  Quantum effects become apparent on a macroscopic scale.
      \end{itemize}
      \item  Fritz London proposed BEC as a mechanism for superfluidity in 4He and superconductivity.
      \end{enumerate}
  \end{column}
 \end{columns}
 \end{frame}

 \begin{frame}
   \frametitle{Experimental evidence of BEC}
   \begin{columns}
   \begin{column}{0.6\textwidth}
      \begin{itemize}
       \item Kapitsa, Allen and Misener discovered He-4 $\Rightarrow$ superfluid, at $T < 2.17$ \textdegree K ($\lambda$ point).
       \item First "pure" $BEC$ was created by Cornell and Wieman $\sim$ dilute vapor $\sim 2000$ Rb-87 atoms $T < 170 \ nK$.
       \item $BEC$ applies to quasiparticles (solids). A magnon in an antiferromagnet (S=1)-Bose–Einstein statistics.
       \end{itemize}
   \end{column}
   \begin{column}
    \begin{center}
       \includegraphics[width=0.6\textwidth]{pictures/BEC1.jpg}
     \end{center}
   \end{column}
   \end{columns}
 \end{frame}

\end{document}

Best Answer

The second column environment in the second big frame of the posted code misses the width argument. Here's a simplified version with the width provided:

\documentclass{beamer}

\begin{document}

 \begin{frame}
   \frametitle{Experimental evidence of BEC}
   \begin{columns}
   \begin{column}{0.6\textwidth}
      \begin{itemize}
       \item Kapitsa, Allen and Misener discovered He-4 $\Rightarrow$ superfluid, at $T < 2.17$  K ($\lambda$ point).
       \item First "pure" $BEC$ was created by Cornell and Wieman $\sim$ dilute vapor $\sim 2000$ Rb-87 atoms $T < 170 \ nK$.
       \item $BEC$ applies to quasiparticles (solids). A magnon in an antiferromagnet (S=1)-Bose–Einstein statistics.
       \end{itemize}
   \end{column}
   \begin{column}{0.4\textwidth}
    \begin{center}
      Test text for the second column.
     \end{center}
   \end{column}
   \end{columns}
 \end{frame}

\end{document}
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