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\DOI{10.5802/crmeca.289}
\datereceived{2025-02-13}
\dateaccepted{2025-02-13}
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\dateposted{2025-03-07}
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\title{Foreword to the special issue ``Recent advances in general
relativity: an issue in memory of Yvonne Choquet-Bruhat''}

\alttitle{Avant-propos du num\'ero sp\'ecial 
\og Avanc\'ees r\'ecentes
dans le domaine de la relativit\'e g\'en\'erale: num\'ero en l'honneur
d'Yvonne Choquet-Bruhat\fg{}}

\author{\firstname{J\'er\'emie} \lastname{Szeftel}}
\address{CNRS \&amp; Laboratoire Jacques-Louis Lions, Sorbonne universit\'e, France}
\email{jeremie.szeftel@sorbonne-universite.fr}

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\xfigure{fx01}{Yvonne Choquet-Bruhat (Photo credit: Genevi\`eve Choquet)}

{\vspace*{1pc}}

The present volume is dedicated to the memory of Yvonne Choquet-Bruhat
who recently passed away at 101 years old. She was the first woman
elected at the French Academy of Sciences and a  remarkable
mathematician. She pioneered the field of mathematical general
relativity with her seminal 1952 paper~\cite{1} on the local
solvability of the Einstein equations. Her subsequent influential works
on the constraint equations and on the evolution problem have left a
deep impact on both theoretical and numerical developments. Her
textbook~\cite{2} is widely viewed as a classical reference
on the subject and an invaluable source of fruitful research
directions. For~more on the work of Yvonne Choquet-Bruhat, we refer the
reader to the text ``On Yvonne'' written by Piotr Chru\'sciel in her
honor for this special issue. We also recommend her
memoirs~\cite{3} for the witty account of a woman
mathematician at a time where they were very few. 

The volume consists of a collection of reviews on various aspects of
general relativity from a mathematical perspective, many of them
originating from the work of Yvonne Choquet-Bruhat. The following
topics are covered: 

\begin{enumerate}[(1)]
\item 
``A survey on the positive mass theorem for asymptotically flat initial
data sets'' by Lan-Hsuan Huang
\item 
``Gluing for the Einstein constraint equations'' by Justin Corvino
\item 
``The stability of Minkowski space and its influence on the
mathematical analysis of general relativity'' by Jacques Smulevici
\item 
``The black hole stability problem'' by Sergiu Klainerman
\item 
``On the regularity problems of the Einstein equations'' by Qian Wang
\item 
``Weak Cosmic Censorship, trapped surfaces, and naked singularities for
the Einstein vacuum equations'' by Yakov Shlapentokh-Rothman
\item 
``The Strong Cosmic Censorship conjecture'' by Maxime Van de Moortel
\item 
``Cosmology, the Big Bang and the BKL conjecture'' by Hans Ringstr\"om
\item 
``Burnett's conjecture in general relativity'' by Arthur Touati
\item 
``Some aspects of spectral and microlocal methods in general
relativity'' by Dietrich H\"afner.
\end{enumerate}

We hope that these surveys will allow the reader to gain insights into
the latest developments of the field, as well as to appreciate the
tremendous achievements that have been obtained along the way, starting
with the pioneering contributions of Yvonne Choquet-Bruhat. 

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