diff --git a/isospectral.tex b/isospectral.tex
index 034ad31..2259db0 100644
--- a/isospectral.tex
+++ b/isospectral.tex
@@ -44,7 +44,7 @@
 
 \begin{frame}{The silver lining}
 	\begin{itemize}
-		\item Isospectral pairs are intriguing in their own right, but they cannot occur in dimension $3$.
+		\item Isospectral manifolds are intriguing in their own right, but in dimension 3 all isospectral manifolds are isometric.
 		\item We can thus attempt to infer the shape of our universe based on its spectrum.
 	\end{itemize}
 \end{frame}
diff --git a/main.tex b/main.tex
index ed55636..34a0d48 100644
--- a/main.tex
+++ b/main.tex
@@ -44,9 +44,9 @@ code-for-last-col = \color{blue}
 }
 
 
-\title{Computing CMB temperature fluctuations for spherical spaces}
+\title{Computing CMB Temperature Fluctuations for Spherical Spaces}
 \author{Adriel Matei, Béla Schneider, Javier Vela, Juš Kocutar}
-%\institute{Presenting: Javier, Juš}
+\institute{University of Groningen}
 
 
 \date{March 24, 2025}
@@ -97,7 +97,7 @@ code-for-last-col = \color{blue}
 			      (\Delta + E_{\textcolor{red}{\beta}}^{\textcolor{blue}{M}})\psi_{\textcolor{red}{\beta}}^{{\textcolor{blue}{M}}, i} = 0.
 		      \end{align*}
 		      \pause
-		\item In fact $E_{\textcolor{red}{\beta}}^m = {\textcolor{red}{\beta}}^2-1$ for $\textcolor{red}{\beta} \in \mathbb{N}$. We call $\textcolor{red}{\beta}$ a wave number.
+		\item In fact $E_{\textcolor{red}{\beta}}^M = {\textcolor{red}{\beta}}^2-1$ for $\textcolor{red}{\beta} \in \mathbb{N}$. We call $\textcolor{red}{\beta}$ a wave number.
 		      \pause
 		\item The set of all possible wave numbers [for which a nonzero solution exists] depends on $\Gamma$ - usually a proper subset of $\mathbb{{N}}$.
 		      \pause
@@ -141,6 +141,7 @@ code-for-last-col = \color{blue}
 \begin{frame}{Inhomogeneous spherical space}
 
 	\begin{itemize}
+        \pause
 		\item Manifolds of the form $\S^3/\Gamma$ with $\Gamma$ a group acting on $\S^3$.
 		\item \textcolor{red}{Multi-connected} space: it has non-contractable loops.
 		\item \textcolor{red}{Inhomogeneous} space: it does not look identical from every point in space.
@@ -170,7 +171,7 @@ code-for-last-col = \color{blue}
 			      \Delta T(\hat{n}) = \sum_{\ell=0}^{\infty} \sum_{m=-\ell}^{\ell} \textcolor{blue}{a_{\ell m}}  Y_{\ell m}(\hat{n})
 		      \]
 		      \pause
-		\item If the universe is isotropic, the \textbf{mean of the harmonic coefficients} should satisfy:
+		\item If the universe is \textcolor{red}{isotropic, the \textbf{mean of the harmonic coefficients} should satisfy:
 		      \[
 			      \langle \textcolor{blue}{a_{\ell m}}  \rangle = 0
 		      \]
@@ -227,7 +228,7 @@ code-for-last-col = \color{blue}
 		\textbf{Possible Explanations:}
 		\begin{itemize}
 			\item A real cosmological signal? → A finite universe or new physics.
-			\item A systematic effect? → Foreground contamination or instrumental noise.
+			\item A systematic effect? → Technological or theory related limitations.
 		\end{itemize}
 	\end{columns}
 \end{frame}
diff --git a/prerequisites.tex b/prerequisites.tex
index cef5766..0df25fc 100644
--- a/prerequisites.tex
+++ b/prerequisites.tex
@@ -3,7 +3,7 @@
 	\begin{figure}[H]
 		\centering
 		\includegraphics[width=0.5\linewidth]{mug-neighbourhoods.png}
-		\caption{The prototypical example of a manifold a mug [13].}
+		\caption{The prototypical example of a manifold -- a mug [13].}
 		\label{fig:mug-neighbourhoods}
 	\end{figure}
 	\pause