Add a gitignore

.gitignore

@@ -0,0 +1,13 @@
+*.aux
+*.bbl
+*.blg
+*.fdb_latexmk
+*.fls
+*.log
+*.out
+*.synctex
+*.synctex(busy)
+main.pdf
+paper.pdf
+technology.pdf
+*.synctex.gz

main.tex

@@ -1,5 +1,5 @@
 \documentclass{beamer}
-\usetheme{Warsaw}  
+\usetheme{Warsaw}
 \usecolortheme{lily}
 
 
@@ -34,7 +34,7 @@ code-for-last-col = \color{blue}
 %\institute{Presenting: Javier, Juš}
 
 
-\date{March 24, 2025} 
+\date{March 24, 2025}
 
 \DeclareMathOperator{\cl}{cl}
 \DeclareMathOperator{\rank}{r}
@@ -50,7 +50,7 @@ code-for-last-col = \color{blue}
         \item Part 1
         \item Part 2
         \item Part 3
-        \item etc   
+        \item etc
     \end{enumerate}
 \end{frame}
 
@@ -59,7 +59,7 @@ code-for-last-col = \color{blue}
 \begin{itemize}
     \item 1
     \item 2
-\end{itemize}  
+\end{itemize}
 
 \end{frame}
 
@@ -78,7 +78,7 @@ code-for-last-col = \color{blue}
 \item Helmholtz equation on $M$ given by
 $$(\Delta + E_\beta^M)\psi_\beta^{M, i} = 0$$
 
-\item In fact $E_\beta^m = \beta^2-1$ for $\beta \in \mathbb{N}$ we call $\beta$ a wave number 
+\item In fact $E_\beta^m = \beta^2-1$ for $\beta \in \mathbb{N}$ we call $\beta$ a wave number
 
 \item The set of all possible wave numbers [for which there exists a non-zero solution] depends on $H$
 
@@ -88,7 +88,7 @@ $$(\Delta + E_\beta^M)\psi_\beta^{M, i} = 0$$
 
 
 \begin{comment}
-    
+
 \begin{frame}[fragile]{CMB Anisotropy of Homogeneous Spherical Spaces}
 \begin{itemize}
 \item If $H = \{1\}$ the set of wave numbers is $\mathbb{N}$
@@ -103,14 +103,14 @@ $$(\Delta + E_\beta^M)\psi_\beta^{M, i} = 0$$
 \begin{frame}[fragile]{CMB Anisotropy of Homogeneous Spherical Spaces - Conclusion}
 \begin{itemize}
 \item For the majority of groups $H$ the anisotropies $\frac{\delta T}{T}$ do not coincide with observations
-\item The only for which it does are $H = O^*$ and $H = I^*.$ the \textit{binary octahedral} and \textit{binary icosahedral} groups of order 48 and 120 
+\item The only for which it does are $H = O^*$ and $H = I^*.$ the \textit{binary octahedral} and \textit{binary icosahedral} groups of order 48 and 120
 
 
 \end{itemize}
 \begin{figure}[H]
 	\centering
 \includegraphics[width=0.4\linewidth]{binary-octahedron.png}
-	\caption{Graphical representation of the binary tetrahedral group 
+	\caption{Graphical representation of the binary tetrahedral group
     [5]}
 	\label{fig:binary-octahedron}
 \end{figure}
@@ -163,7 +163,7 @@ $$(\Delta + E_\beta^M)\psi_\beta^{M, i} = 0$$
 
 \begin{frame}{References}
     \begin{itemize}
- 
+
         \item N. Jarosik et. al. \textit{Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results}. The American Astronomical Society, 2011.
         \item M. Herlihy and N. Shavit. \textit{The Topological Structure of Asynchronous Computability}. Journal of the ACM, 1996.
         \item A. Ikeda. \textit{On the spectrum of a Riemannian manifold of positive constant curvature}. Osaka Journal of Mathematics, 1980.
@@ -185,7 +185,7 @@ $$(\Delta + E_\beta^M)\psi_\beta^{M, i} = 0$$
 \begin{frame}{}
 \begin{center}
 \huge Thank You!
-\end{center}    
+\end{center}
 \end{frame}
 
 \end{document}