diff --git a/isospectral.tex b/isospectral.tex index 7e67087..ffb2fae 100644 --- a/isospectral.tex +++ b/isospectral.tex @@ -32,16 +32,20 @@ \end{frame} \end{comment} -\begin{frame}{The silver lining} +{ +\usebackgroundtemplate{ \begin{tikzpicture} \clip (0,0) rectangle (\paperwidth,\paperheight); - \fill[color=orange] (\paperwidth-10pt,0) rectangle (\paperwidth,\paperheight); + \fill[color=silver] (\paperwidth-10pt,0) rectangle (\paperwidth,\paperheight); % Added - \fill[color=orange](0,0) rectangle (10pt,\paperheight); + \fill[color=silver](0,0) rectangle (10pt,\paperheight); \end{tikzpicture} +} + +\begin{frame}{The silver lining} \begin{itemize} - \item Isospectral pairs are cool and all, but they cannot occur in dimension $3$. \item We can thus attempt to infer the shape of our universe based on its spectrum. \end{itemize} \end{frame} +} diff --git a/main.pdf b/main.pdf index e42e8d0..9f4b988 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.tex b/main.tex index 9712192..28a85c2 100644 --- a/main.tex +++ b/main.tex @@ -61,6 +61,8 @@ code-for-last-col = \color{blue} \setbeamercolor{block body}{fg=black, bg=pink!20} \setbeamercolor{titlebox}{fg=black,bg=white} +\definecolor{silver}{RGB}{192, 192, 192} + \begin{document} \section{Introduction} @@ -136,7 +138,7 @@ code-for-last-col = \color{blue} \item Manifolds of the form $\S^3/\Gamma$ with $\Gamma$ a group acting on $\S^3$. \item Multi-connected space: it has non-contractable loops. \item Inhomogeneous space: it does not look identical from every point in space. - \pause + \pause \item Fixing $|\Gamma|=8$, we have three multi-connected manifolds, up to equivalence: \pause \begin{enumerate} \item homogeneous: $N3$ and $L(8,1)$. @@ -230,16 +232,16 @@ code-for-last-col = \color{blue} \pause \begin{enumerate} - \item We can infer the shape of the universe from its spectrum. + \item We can infer the shape of the universe from its spectrum. -\pause - \item There are two homogeneous spherical manifolds obtained as $\S^3/\Gamma$ which produce CMB similar to observations. + \pause + \item There are two homogeneous spherical manifolds obtained as $\S^3/\Gamma$ which produce CMB similar to observations. -\pause - \item Inhomogeneous spherical spaces exhibit varied behavior of CMB anisotropies. + \pause + \item Inhomogeneous spherical spaces exhibit varied behavior of CMB anisotropies. -\pause - \item Statistical test results suggest possibilities of finite multi-connected topology. + \pause + \item Statistical test results suggest possibilities of finite multi-connected topology. \end{enumerate} \end{frame}