From fc67d22c14dfed5241b56c8dc26ff14d5573d4f7 Mon Sep 17 00:00:00 2001
From: "juso.koc" <juso.koc@gmail.com>
Date: Fri, 21 Mar 2025 14:01:05 +0000
Subject: [PATCH] Update on Overleaf.
---
isospectral.tex | 2 +-
main.tex | 7 ++++---
prerequisites.tex | 2 +-
3 files changed, 6 insertions(+), 5 deletions(-)
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 480c094..597aad4 100644
--- a/main.tex
+++ b/main.tex
@@ -45,7 +45,7 @@ code-for-last-col = \color{blue}
\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}
@@ -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.
\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
@@ -140,6 +140,7 @@ 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.
@@ -226,7 +227,7 @@ 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 b53307a..822de1b 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