\documentclass{memoires}
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\title{Mapping Class Groups \\ \& \\ their Representations}
\author{Thiago Brevidelli Garcia}
\dedication{This Master's Thesis is dedicated to my dear friend Lucas Schiezari. \\ May he rest in peace.}

\begin{document}

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\begin{about}
  This is my M2 Mémoire (Master's Thesis), written in June 2024 under the
  supervision of Professor Maxime Wolff of the Institut of Mathématiques de
  Toulouse (IMT), France. The subject of the dissertation at hand is the notion
  of the mapping class group of a surface, their linear representations and
  some recent developments in the field. Namely, we discuss Korkmaz' proof of
  the triviality of low-dimensional representations.

  Throughout these notes we will follow some guiding principles. First, lengthy
  proofs are favored over collections of smaller lemmas. This is a deliberate
  effort to emphasize the relevant results. That said, this dissertation is
  intended to be concise. Hence numerous results are left unproved. We refer
  the reader to proofs in other materials when appropriate.

  Our main references are the beautiful book by Farb-Margalit
  \cite{farb-margalit}, as well as the 2023 article by Korkmaz \cite{korkmaz}.
  We assume the reader is already familiar with basic topology and group
  theory. Crucially, we \emph{do not} assume any familiarity with
  representation theory. Because of tight deadlines, we have opted to
  hand-draw all the figures.

  \section*{Acknowledgments}

  I would like to thank my friends and family for their tireless love and
  support. Special thanks to my girlfriend for her encouragement and
  understanding during this challenging year. I extend my gratitude to
  Professor Wolff for accepting me as his student and providing me with his
  invaluable guidance. I should also thank Matthieu Faitg for his help with the
  discussion on TQFT representations.

  \section*{License}

  This document was typeset and compiled using free software. Its \LaTeX~source
  code is freely available at \url{https://git.pablopie.xyz/memoire-m2}, for
  distribution under the terms of the
  \href{https://creativecommons.org/licenses/by/4.0/}{Creative Commons
  Attribution 4.0 license}.
\end{about}

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\input{sections/representations}

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nt}

