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\begin{document}
\title{Topological origins of gravitational lensing}
\author[1]{Alex Leviyev}
\affil[1]{Center for Gravitational Physics, University of Texas at Austin}
\date{\today}
% \tableofcontents
\maketitle

\begin{abstract}
Deflection of light by massive objects is of significant practical interest in astrophysics \cite{congdon2018principles}. Applications range from constraining cosmological parameters to studying the distribution of dark matter in galaxies. In this note we review a recent result that illustrates gravitational lensing is an inherently topological effect \cite{Gibbons_2008}. We briefly review Fermat's principle, optical geometry, and other relevant results before introducing the so called Gauss-Bonnet theorem. Our discussion will conclude with a result showing how gravitational lensing necessarily requires nontrivial spacetime topology.
% High-precision posterior exploration forms the backbone of many scientific and engineering disciplines, e.g astronomy. Popular tools used for such tasks are often based on the tried and true Metropolis-Hastings algorithm--a \textit{stochastic} procedure that simulates a Markov chain that is gauranteed to explore the target. However, simulating such a Markov chain for problems with computationally expensive physical models or large datasets is often infeasible. Stein variational gradient descent (SVGD) is an alternative that has recently blown up in popularity due to its tractability
\end{abstract}

% \section{Intro}
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\end{document}