diff --git a/isospectral.tex b/isospectral.tex index 7cab952..49ea7c1 100644 --- a/isospectral.tex +++ b/isospectral.tex @@ -44,7 +44,7 @@ \begin{frame}{The silver lining} \begin{itemize} - \item Isospectral pairs are cool and all, but they cannot occur in dimension $3$. + \item Isospectral pairs are intriguing in their own right, but they cannot occur in dimension $3$. \item We can thus attempt to infer the shape of our universe based on its spectrum. \end{itemize} \end{frame} diff --git a/main.pdf b/main.pdf index d719bba..0b659f2 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.tex b/main.tex index ae6c2eb..2babbeb 100644 --- a/main.tex +++ b/main.tex @@ -263,7 +263,7 @@ code-for-last-col = \color{blue} \end{frame} -\begin{frame}{References} +\begin{frame}{References 2 --- electric boogaloo} \begin{itemize} \item [6] 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. @@ -274,7 +274,7 @@ code-for-last-col = \color{blue} \end{itemize} \end{frame} -\begin{frame}{References} +\begin{frame}{References 3 --- the references strike again} \begin{itemize} \item [11] E. A. Lauret and B. Linowitz. \textit{The spectral geometry of hyperbolic and spherical manifolds: analogies and open problems}. New York Journal of Mathematics, 2025. \item [12] R. Lehoucq, J. Weeks, J. P. Uzan, E. Gausmann, and J.P. Luminet. \textit{Eigenmodes of three-dimensional spherical spaces and their application to cosmology}. Classical and Quantum Gravity, 2002.