memoire-m2

My M2 Memoire on mapping class groups & their representations

git clone: git://git.pablopie.xyz/memoire-m2
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Commit: 77470324c188900794b90388126a34b72c3466be
Parent: 1b87dd5efb423ad25ae23786afc7942dd938a8dd
Author: Pablo <pablo-pie@riseup.net>
Date: Sat, 22 Jun 2024 13:02:43 +0000

Wrote the "About" section

Diffstat

1 file changed, 17 insertions, 12 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/preface.tex	29	17	12

diff --git a/sections/preface.tex b/sections/preface.tex
@@ -2,25 +2,30 @@
 
 \thispagestyle{empty}
 
-% TODO: Say this is my memoire
-% TODO: Explain we will dive into Korkmaz' paper
+This is my M2 Memoir (Master 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.
 
-% TODO: Say that we have no space for most proofs
 Throughout these notes we will follow some guiding principles. First, lengthy
 proofs are favored as opposed to collections of smaller lemmas. This is a
-deliberate effort to emphasize the relevant results. Secondly, and this is more
-proofs can sometimes feel like an unmotivated pile of technical arguments.
-Instead, we prefer to focus on the intuition behind the relevant results.
+deliberate effort to emphasize the relevant results. That said, this
+dissertation is meant to be concise. Hence numerous results are left unproved.
+We refer the reader to proofs in other materials when appropriate.
 
-% TODO: Say what you assume
+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.
+Cruacially, we \emph{do not} assume any familiarity with representation-theory.
 
 \section*{Acknowledgments}
 
-% TODO: Thank my girlfriend
-I would like to thank my family for their tireless love and
-support. I would also like to thank my dear friend Lucas Dias Schiezari for
-somehow convincing me to apply for a bachelors degree in pure mathematics, as
-well as the moments of joy we shared. May he rest in peace.
+I would like to thank my friends and family for their tireless love and
+support. Special thanks to my girlfriend for her endless encouragement and
+understanding during this challenging year. I should also thank M. Faitg for
+his help with the discussion on TQFT representations.
 
 \section*{License}