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juso.koc 2025-03-21 14:01:05 +00:00 committed by node
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3 changed files with 6 additions and 5 deletions

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isospectral.tex
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@ -44,7 +44,7 @@
\begin{frame}{The silver lining} \begin{frame}{The silver lining}
\begin{itemize} \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. \item We can thus attempt to infer the shape of our universe based on its spectrum.
\end{itemize} \end{itemize}
\end{frame} \end{frame}

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main.tex
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@ -45,7 +45,7 @@ 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} \author{Adriel Matei, Béla Schneider, Javier Vela, Juš Kocutar}
\institute{Presenting: Javier, Juš} \institute{University of Groningen}
\date{March 24, 2025} \date{March 24, 2025}
@ -96,7 +96,7 @@ code-for-last-col = \color{blue}
(\Delta + E_{\textcolor{red}{\beta}}^{\textcolor{blue}{M}})\psi_{\textcolor{red}{\beta}}^{{\textcolor{blue}{M}}, i} = 0. (\Delta + E_{\textcolor{red}{\beta}}^{\textcolor{blue}{M}})\psi_{\textcolor{red}{\beta}}^{{\textcolor{blue}{M}}, i} = 0.
\end{align*} \end{align*}
\pause \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 \pause
\item The set of all possible wave numbers [for which a nonzero solution exists] depends on $\Gamma$ - usually a proper subset of $\mathbb{{N}}$. \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 \pause
@ -140,6 +140,7 @@ code-for-last-col = \color{blue}
\begin{frame}{Inhomogeneous spherical space} \begin{frame}{Inhomogeneous spherical space}
\begin{itemize} \begin{itemize}
\pause
\item Manifolds of the form $\S^3/\Gamma$ with $\Gamma$ a group acting on $\S^3$. \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}{Multi-connected} space: it has non-contractable loops.
\item \textcolor{red}{Inhomogeneous} space: it does not look identical from every point in space. \item \textcolor{red}{Inhomogeneous} space: it does not look identical from every point in space.
@ -226,7 +227,7 @@ code-for-last-col = \color{blue}
\textbf{Possible Explanations:} \textbf{Possible Explanations:}
\begin{itemize} \begin{itemize}
\item A real cosmological signal? → A finite universe or new physics. \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{itemize}
\end{columns} \end{columns}
\end{frame} \end{frame}

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prerequisites.tex
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@ -3,7 +3,7 @@
\begin{figure}[H] \begin{figure}[H]
\centering \centering
\includegraphics[width=0.5\linewidth]{mug-neighbourhoods.png} \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} \label{fig:mug-neighbourhoods}
\end{figure} \end{figure}
\pause \pause