Merge branch 'master' of https://git.overleaf.com/67dbe68df0414d63b309f98a

isospectral.tex

@@ -7,10 +7,10 @@
 				\Delta f \coloneq \divergence \nabla f.
 			\end{align*}
 		\end{definition}
-		\item The spectrum of this operator is a subset of $[0, \infty)$. We call it the \emph{spectrum} of the manifold.
+		\item The spectrum of this operator is a subset of $[0, \infty)$. We call it the \textcolor{blue}{\emph{spectrum}} of the manifold.
 		      \pause
 		\item The spectrum determines many things about the space (like its volume).
-		\item When two distinct (up to isomorphism) manifolds share a spectrum, they for an \emph{isospectral pair}.
+		\item When two distinct (up to isomorphism) manifolds share a spectrum, they for an \textcolor{red}{\emph{isospectral pair}}.
 	\end{enumerate}
 \end{frame}
 

prerequisites.tex

@@ -20,10 +20,10 @@
 \begin{frame}{Quotients of the $3$-sphere}
 	\begin{itemize}
 		\item $\so 4$ is isomorphic to the isometry group of $\S^3$.
-		\item Subgroups $\Gamma \leqslant \so 4$ define equivalence classes of orbits on $\S^3$ by the standard action of $\so 4$ on $\R^4$, i.e. $x \sim y$ iff $x = My$ for some $M \in \Gamma$.
+		\item Subgroups $\Gamma \leqslant \so 4$ define \textcolor{darkyellow}{equivalence classes} of orbits on $\S^3$ by the standard action of $\so 4$ on $\R^4$, i.e. $x \sim y$ iff $x = My$ for some $M \in \Gamma$.
 		      \pause
 		\item The obtain space is (\emph{sometimes}) a manifold. In particular, it is well defined and spherical for finite $\Gamma$.
-		\item This can be easily generalised to the $n$-sphere.
+		\item This can be easily generalized to the $n$-sphere.
 	\end{itemize}
 \end{frame}