From 1eac83d4a9c342cb273ccaa6326719d82f2986d3 Mon Sep 17 00:00:00 2001
From: prescientmoon <git@moonythm.dev>
Date: Fri, 21 Mar 2025 13:11:10 +0100
Subject: [PATCH] Add silver lining

---
 isospectral.tex |  12 ++++++++----
 main.pdf        | Bin 1350989 -> 1342439 bytes
 main.tex        |  18 ++++++++++--------
 3 files changed, 18 insertions(+), 12 deletions(-)

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 e42e8d084a4a4502a9c8843a95ec54f2b66035dc..9f4b9887b2accef9b25ae1c3a895cb4a88ff86fb 100644
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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}