Add some missing dots at the end

main.tex

@@ -90,7 +90,7 @@ code-for-last-col = \color{blue}
 \begin{frame}[fragile]{Homogeneous Spherical Spaces}
 	\begin{itemize}
 		\pause
-		\item Finite subgroup $\Gamma \leq \so 4.$
+		\item Finite subgroup $\Gamma \leqslant \so 4.$
 		      \pause
 		\item The Helmholtz equation on $\textcolor{blue}{M}$ has the spectrum of the underlying manifold as its solutions, and is given by
 		      \begin{align*}
@@ -168,18 +168,18 @@ code-for-last-col = \color{blue}
 		\pause
 		\item The CMB temperature fluctuations can be expanded as:
 		      \[
-			      \Delta T(\hat{n}) = \sum_{\ell=0}^{\infty} \sum_{m=-\ell}^{\ell} \textcolor{blue}{a_{\ell m}}  Y_{\ell m}(\hat{n})
+			      \Delta T(\hat{n}) = \sum_{\ell=0}^{\infty} \sum_{m=-\ell}^{\ell} \textcolor{blue}{a_{\ell m}}  Y_{\ell m}(\hat{n}).
 		      \]
 		      \pause
-		\item If the universe is \textcolor{red}{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
 		      \[
-			      \langle \textcolor{blue}{a_{\ell m}}  \rangle = 0
+			      \langle \textcolor{blue}{a_{\ell m}}  \rangle = 0.
 		      \]
 	\end{itemize}
 	\pause
 	\textbf{Key Question:}
-	- Does the observed CMB data deviate from statistical isotropy?
+	Does the observed CMB data deviate from statistical isotropy?
-	- If \( \langle \textcolor{blue}{a_{\ell m}} \rangle \neq 0 \), this suggests a preferred cosmic direction.
+	If \( \langle \textcolor{blue}{a_{\ell m}} \rangle \neq 0 \), this suggests a preferred cosmic direction.
 \end{frame}
 
 \begin{frame}{Methodology: Sky Masking and the Test Statistic}
@@ -192,7 +192,7 @@ code-for-last-col = \color{blue}
 		      \pause
 		\item The test statistic \( S_i \) is used, with a matrix $W$ to correct for these effects:
 		      \[
-			      S_i = \sum_{j} W_{ij} M_j
+			      S_i = \sum_{j} W_{ij} M_j.
 		      \]
 	\end{itemize}
 	\pause
@@ -201,7 +201,7 @@ code-for-last-col = \color{blue}
 		\item We generate thousands of \textbf{simulated CMB skies} assuming isotropy.
 		\item Each sky has different random \( a_{\ell m} \), drawn from:
 		      \[
-			      \textcolor{blue}{a_{\ell m}}  \sim \mathcal{N} (0, C_\ell)
+			      \textcolor{blue}{a_{\ell m}}  \sim \mathcal{N} (0, C_\ell).
 		      \]
 		\item The observed WMAP data is compared against these simulations.
 	\end{itemize}