Very last changes

.gitignore

@@ -16,3 +16,4 @@
 *.synctex(busy)
 *.synctex.gz
 *.toc
+*.xlsx

.vscode/ltex.dictionary.en-US.txt

@@ -58,3 +58,33 @@ Goresky
 Schottky
 Calabi
 Yau
+Tian
+Brendle
+Guenancia
+Biquard
+Fano
+anticanonical
+orbifold
+Eyssidieux
+Guedj
+Zeriahi
+Kolodziej
+Cho
+Choi
+Hein
+smoothable
+Datar
+Fu
+Delcroix
+Székelyhidi
+Tosatti
+Chiu
+Oberwolfach
+Conlon
+Daskalopoulos
+Mese
+Nevanlinna
+arithmetics
+Grauert
+Mok
+regionality

.vscode/ltex.hiddenFalsePositives.en-US.txt

@@ -1,3 +1,4 @@
 {"rule":"PREPOSITION_VERB","sentence":"^\\QProbably the most complete result in this field is due to A. Bloch (more than 100 years ago), who -in modern language- showed that the Zariski closure of a map \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q to a complex torus \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is the translate of a sub-tori.\\E$"}
 {"rule":"PREPOSITION_VERB","sentence":"^\\QIts beginnings date back to 1926, when André Bloch showed that the Zariski closure of entire holomorphic curve \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q to a complex torus \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is the translate of a sub-torus.\\E$"}
 {"rule":"MISSING_GENITIVE","sentence":"^\\QHodge modules are used to define generalizations of well-known ideals of singularities, such as multiplier ideals from analysis and algebraic geometry.\\E$"}
+{"rule":"MORFOLOGIK_RULE_EN_US","sentence":"^\\QThe workshop has a distinguished history, originating with Grauert and Remmert.\\E$"}

MFO26.tex

@@ -3,6 +3,7 @@
 %
 % Local font definitions -- need to come first
 %
+\usepackage{amsthm}
 \usepackage{libertine}
 \usepackage[libertine]{newtxmath}
 
@@ -20,6 +21,8 @@
 
 \sloppy
 
+\newtheorem*{q}{Question}
+
 % Colours for hyperlinks
 \definecolor{lightgray}{RGB}{220,220,220}
 \definecolor{gray}{RGB}{180,180,180}
@@ -51,31 +54,231 @@
 \maketitle
 
 
+\section{Title and proposed organizers}
+
+\subsection{Workshop Title}
+
+Komplexe Analysis --- Analytic and Algebraic Methods in the Theory of Kähler Spaces
 
 
+\subsection{Proposed Organizers}
 
+\begin{tabular}{ll}
+  \parbox[t]{7cm}{
+    Eleonora Di Nezza\\
+    IMJ-PRG, Sorbonne Université,\\
+    4 Place Jussieu\\
+     75005 Paris\\
+      France\\[2mm]
+    \href{mailto:eleonora.dinezza@imj-prg.fr}{eleonora.dinezza@imj-prg.fr}} &
+  \parbox[t]{7cm}{
+    Stefan Kebekus\\
+    Albert-Ludwigs-Universität Freiburg\\
+    Ernst-Zermelo-Straße 1\\
+    79104 Freiburg\\
+    Germany\\[2mm]
+    \href{mailto:stefan.kebekus@math.uni-freiburg.de}{stefan.kebekus@math.uni-freiburg.de}}    
+    \\
+  \ \\
+  \ \\
+ \parbox[t]{6cm}{
+    Mihai Păun \\
+    Universität Bayreuth \\
+    Universitätsstraße 30\\
+    95447 Bayreuth\\
+    Germany\\[2mm]
+    \href{mailto:mihai.paun@uni-bayreuth.de}{mihai.paun@uni-bayreuth.de}}
+ &
+  \parbox[t]{6cm}{
+    Stefan Schreieder\\
+    Leibniz Universit\"at Hannover \\
+    Welfengarten 1\\
+    30167 Hannover\\
+    Germany\\[2mm]
+    \href{mailto:schreieder@math.uni-hannover.de}{schreieder@math.uni-hannover.de}}
+\end{tabular}
+\clearpage
+
+\section{Abstract}
+
+The proposed workshop will present recent advances in the analytic and algebraic
+study of Kähler spaces. Key topics to be covered include:
+\begin{itemize}
+\item Canonical metrics and their limits,
+
+\item Hyperbolicity properties of complex algebraic varieties,
+
+\item The topology and Hodge theory of Kähler spaces.
+\end{itemize} 
+While these topics are classical, various breakthroughs were achieved only
+recently.  Moreover, each is closely linked to various other branches of
+mathematics.   For example, geometric group theorists have recently applied
+methods from complex geometry and Hodge theory to address long-standing open
+problems in geometric group theory.  Similarly, concepts used in the framework
+of hyperbolicity questions, such as entire curves, jet differentials and
+Nevanlinna theory have recently seen important applications in the study of
+rational and integral points in number theory. To foster further
+interdisciplinary collaboration, we will invite several experts from related
+fields to participate in the workshop.
+
+The workshop has a distinguished history, originating with Grauert and Remmert.
+The 2026 edition brings in new organizers with fresh perspectives.  About half
+of the proposed participants have not attended this workshop before. To ensure a
+smooth transition, we decided to retain two of the established organizers for
+this application; we plan to replace both of them in the next application for
+2029.
+
+
+\section{Mathematics Subject Classification}
+
+\subsubsection*{2020 Mathematics Subject Classification}
+
+\begin{tabular}{llll}
+Primary   & 32 &--& Several complex variables and analytic spaces\\
+Secondary & 14 &--& Algebraic geometry \\
+          & 53 &--& Differential geometry \\
+          & 58 &--& Global analysis, analysis on manifolds 
+\end{tabular}
 
 
 \section{Description of the Workshop}
 
 
-% Topology of Kähler spaces: D-modules, perverse sheaves, Hodge modules
+The proposed workshop presents recent results in Complex Geometry and Kähler
-%
+spaces, focusing on a combination of analytic and algebraic methods. We aim to
-%  
+emphasize the fields described below, each rooted in complex analysis and
-%- Singularities and Hodge ideals etc: Mustata-Popa, Park, Ruijie Yang, Schnell 
+interconnected with various other branches of mathematics.
-%
+
-%- Lagrangian fibrations: Maulik-Shen, Shen-Yin, Schnell, Bakker
+An important goal of our workshop is to foster collaborations between
-%
+mathematicians from different communities, with diverse backgrounds and
-%- Singer-Hopf conjecture and fundamental groups of Kaehler manifolds: Arapura, Botong Wang, Maxim, Llosa-Isenrich—Py.
+perspectives. We have invited experts from related fields, and we will ask them
+to give survey talks on their work early in the week. This will allow them to
+introduce themselves to the complex geometers attending the workshop and provide
+ample opportunities for discussions throughout the rest of the week. Following
+the Oberwolfach guidelines, we will keep the number of talks comparatively small
+(no more than 25) to allow for plenty of informal discussions.
+
+One evening during the workshop, we will hold a special session where junior
+participants who are not selected to give a 60-minute talk can give a 5-10
+minute pitch on their work to introduce themselves to the community.
 
 
-\subsection{Topology of Kähler spaces: D-modules, perverse sheaves, Hodge modules}
 
-Over the last decade, Saito's theory of Hodge modules has seen spectacular
+\subsection{Canonical Metrics and Hyperbolicity}
-applications in birational geometry.  More recent developments, which are of
+
-significant importance, connect the theory to singularity theory, commutative
+\subsubsection{Kähler--Einstein Metrics with Conic Singularities and Their Limits}
-algebra, and the topology of algebraic varieties.  The following topics in this
+
-area will particularly interest our workshop.
+In the proof of the Donaldson--Tian--Yau conjecture, which Chen--Donaldson--Sun
+gave in a series of papers around 2015, Kähler--Einstein metrics with conic
+singularities along a smooth divisor emerged to play a vital role.  The work of
+Brendle, Donaldson, Guenancia, Rubinstein, and many others provides a complete
+package of results that generalize Yau's celebrated solution of the Calabi
+conjecture to the conic setting.  Since then, these metrics have become an
+object of study in their own right.  Today, many exciting recent developments in
+this field gravitate around the following general question.
+
+\begin{q}
+  Let $X$ be a projective manifold, and let $D \subsetneq X$ be a non-singular
+  divisor.  Assume that for every sufficiently small angle $0 < \beta \ll 1$,
+  there exists a unique Kähler--Einstein metric $\omega_\beta$ with conic
+  singularities of angle $2\pi\beta$ along $D$.  In other words, assume that
+  \[
+    Ricci_{\omega_\beta}= \lambda \cdot \omega_{\beta}+ (1-\beta)\cdot [D],
+    \quad
+    \text{where } \lambda \in \{ \pm 1\}.
+  \]
+  Is there a meaningful limit of $\omega_\beta$ as $\beta\to 0$, perhaps after
+  rescaling?
+\end{q}
+
+In \cite{zbMATH07615186} and the very recent preprint \cite{arXiv:2407.01150},
+Biquard--Guenancia begin settling relevant (and technically challenging!)
+particular cases of this question.
+\begin{itemize}
+  \item If $(X,D)$ is the toroidal compactification of a ball quotient, then the
+  limit of the metric exists and equals the hyperbolic metric.
+
+  \item If $X$ is Fano and $D$ is a divisor whose class is proportional to the
+  anticanonical class, then the limit of the rescaled metric exists and equals
+  the Tian--Yau metric. 
+\end{itemize}
+More work is ongoing, and we expect to report on substantial progress by the
+time our workshop takes place.
+
+
+\subsubsection{Kähler--Einstein Metrics on Singular Spaces}
+
+Motivated by progress in the Minimal Model Program, there has been increasing
+interest in Kähler--Einstein metrics on singular spaces.  While one of the first
+results in this direction dates back to the early 1970s when Kobayashi
+constructed orbifold Kähler--Einstein metrics, a definitive existence result for
+a relevant class of singularities was obtained by Eyssidieux--Guedj--Zeriahi
+about 15 years ago in \cite{zbMATH05859416}, by combining Yau's technique with
+Kolodziej's $\mathcal C^0$ estimates.  Much more recently, Li--Tian--Wang
+extended Chen-Donaldson-Sun's solution of the Yau--Tian--Donaldson conjecture to
+general $\mathbb Q$-Fano varieties \cite{zbMATH07382001, zbMATH07597119}.
+
+For most applications, it is essential to control the geometry of these metrics
+near the singularities.  Despite the problem's obvious importance, little is
+known so far.  The continuity of the metric's potential has been established
+quite recently in the preprint \cite{arXiv:2401.03935} of Cho--Choi. Beyond
+that, the main progress in this direction is due to Hein--Sun
+\cite{zbMATH06827885}, who showed that near a large class of smoothable isolated
+singularities that are locally isomorphic to a Calabi-Yau cone, the singular
+Calabi-Yau metric must be asymptotic in a strong sense to the Calabi-Yau cone
+metric.  Using the bounded geometry method, Datar--Fu--Song recently showed an
+analogous result in the case of isolated log canonical singularities
+\cite{zbMATH07669617}.  Fu–Hein–Jiang obtained precise asymptotics shortly
+after, \cite{zbMATH07782497}. Essential contributions directly connected to
+these topics are due to Chiu--Székelyhidi \cite{zbMATH07810677}, Delcroix,
+Conlon--Hein \cite{zbMATH07858206}, C.~Li, Y.~Li, Tosatti and Zhang.
+
+
+\subsubsection{Complex Hyperbolicity}
+
+The 1979 Green-Griffiths-Lang conjecture asserts that every complex-projective
+variety $X$ of general type contains a proper subvariety $Y \subsetneq X$, such
+that every non-constant entire holomorphic curve $\mathbb C \to X$ takes its
+values in $Y$.  Its beginnings date back to 1926, when André Bloch showed that
+the Zariski closure of entire holomorphic curve $\varphi: \mathbb C \to A$ to a
+complex torus $A$ is the translate of a sub-torus. Today, the conjecture still
+drives substantial research in complex geometry.  Several authors, including
+Brotbek, Brunebarbe, Deng, Cadorel, and Javanpeykar, opened a new research
+direction with relation to arithmetic, by combining techniques from Hodge theory
+with Nevanlinna theory and jet differentials, \cite{arXiv:2007.12957,
+arXiv:2207.03283, arXiv:2305.09613}. Besides, we highlight two additional
+advances that will be relevant for our workshop.
+
+
+\paragraph{Hypersurfaces in Projective Space}
+
+A remarkable paper of Bérczi and Kirwan, \cite{MR4688701} published in September
+last year, establishes hyperbolicity and proves the Green-Griffiths-Lang for
+generic hypersurfaces of the projective space, $X \subsetneq \mathbb P^n$,
+provided that the degree of $X$ is larger than an explicit polynomial in $n$.
+These are significant improvements of earlier degree bounds, which involve
+non-polynomial bounds of order $(\sqrt{n} \log n)^n$ or worse.  The proof builds
+on a strategy of Diverio-Merker-Rousseau and combines non-reductive geometric
+invariant theory with the ``Grassmannian techniques'' of Riedl-Yang.  A very
+recent preprint of Cadorel simplifies the proof Bérczi-Kirwan substantially, but
+still needs to undergo a peer review, \cite{arXiv:2406.19003}.
+
+
+\paragraph{Representations of Fundamental Groups}
+
+Using recent advances in the theory of harmonic maps due to Daskalopoulos--Mese
+\cite{arXiv:2112.13961}, Deng--Yamanoi were able to confirm the Green--Griffiths
+conjecture for manifolds whose fundamental group admits a representation having
+certain natural properties, in direct analogy to the case of general-type
+curves. 
+
+
+\subsection{Topology and Hodge Theory of Kähler spaces}
+
+Ever since its invention, Hodge theory has been one of the most powerful tools
+in studying the geometry and topology of Kähler spaces.  More recent
+developments connect the theory to singularity theory and commutative algebra.
+The following topics in this area will particularly interest our workshop. 
 
 
 \subsubsection{Singularities and Hodge Ideals}
@@ -98,7 +301,7 @@ program put forward by Friedman--Laza aims at understanding the Hodge structures
 of degenerating Calabi--Yau varieties. 
 
 
-\subsubsection{Lagrangian fibrations}
+\subsubsection{Lagrangian Fibrations}
 
 A Lagrangian fibration of a hyperkähler manifold $M$ is a proper holomorphic map
 $f : M \to B$ whose generic fibers are Langrangian. 
@@ -110,23 +313,27 @@ If $M$ is compact, a well-known conjecture in the field predicts that $B$ is
 projective space.  In the case where $B$ is smooth, Hwang established the
 conjecture more than 16 years ago in a celebrated paper.  There is new insight
 today, as Bakker--Schnell recently found a purely Hodge theoretic proof of
-Hwang's result in \cite{arXiv:2311.08977}.  Hopefully, these methods will give
+Hwang's result in \cite{arXiv:2311.08977}.  On the other hand Li--Tosatti found
-insight into the singular setting, which remains open to date.
+a more differential-geometric argument \cite{zbMATH07863260}, which relied
+heavily on a singular version of Mok's uniformization theorem. Even if both
+methods use results about rational curves, which confines them from the start to
+the smooth case, there is hope that they will give insight into the singular
+setting, which remains open to date.
 
 
 \paragraph{Non-compact Setting}
 
-In the non-compact setting, geometers study Lagrangian fibrations in the
+Geometers study Lagrangian fibrations over non-compact bases in the framework of
-framework of the ``$P=W$ conjecture,'' which Maulik–Shen and
+the ``$P=W$ conjecture,'' which Maulik--Shen and Hausel--Mellit--Minets--Schiffmann
-Hausel–Mellit–Minets–Schiffmann have recently proved \cite{arXiv:2209.02568,
+have recently proved \cite{arXiv:2209.02568, arXiv:2209.05429}.  In the same
-arXiv:2209.05429}.  In the same setting, Shen–Yin discovered a remarkable
+setting, Shen–Yin discovered a remarkable symmetry of certain pushforward
-symmetry of certain pushforward sheaves and conjectured that more general
+sheaves and conjectured that more general symmetries exist. Schnell has recently
-symmetries exist. Schnell has recently established these conjectures in
+established these conjectures in \cite{arXiv:2303.05364} and also proved two
-\cite{arXiv:2303.05364} and also proved two conjectures of Maulik–Shen–Yin on
+conjectures of Maulik–Shen–Yin on the behavior of certain perverse sheaves near
-the behavior of certain perverse sheaves near singular fibers.
+singular fibers.
 
 
-\subsubsection{Singer--Hopf conjecture and fundamental groups of Kähler manifolds}
+\subsubsection{Singer--Hopf Conjecture and Fundamental Groups of Kähler Manifolds}
 
 The Singer-Hopf conjecture asserts that a closed aspherical manifold of real
 dimension $2n$ has positive signed Euler characteristic, $(-1)^n \cdot
@@ -147,130 +354,84 @@ group theory with experts on Hodge theory and to explore further potential
 applications of the methods from one field to problems in the other.
 
 
-\subsection{Canonical metrics and Kobayashi hyperbolicity}
+\section{Suggested and Excluded Dates}
 
-\subsubsection{Kähler-Einstein metrics with conic singularities and their limits}
+We would prefer if our workshop took place in mid of September or early to mid
-
+of April.
-In the proof of Donaldson-Tian-Yau conjecture -around 2015-, the Kähler-Einstein
-metrics with conic singularities along a smooth divisor are playing a key role.
-Since then, they have become an object of study in its own right. For example,
-we currently dispose of results which are completely analog to Yau’s celebrated
-solution of Calabi conjecture in conic setting, by the work of S. Brendle, S.
-Donaldson, H. Guenancia, Y. Rubinstein,  among many others. 
-
-An important number of the exciting recent developments in this field are
-gravitating around the following general question: \emph{let $X$ be a projective
-manifold, and let $D\subset $ be a non-singular divisor. We assume that for each
-angle $0< \beta<< 1$ small enough, there exists a unique KE metric
-$\omega_\beta$ with conic singularities of angle $2\pi\beta$ along $D$, i.e.
-$$Ricci_{\omega_\beta}= \lambda \omega_{\beta}+ (1-\beta)[D],$$
-where $\lambda$ is equal to -1 or 1. Can one extract a limit of $(\omega_\beta)$
-as $\beta\to 0$, eventually after rescaling}?
-
-The series of articles by Biquard-Guenancia —2022 and 2024-- settle many
-interesting and technically challenging particular casses of this question:
-toroidal compactifications of ball quotients -in which the limit mentioned above
-is the hyperbolic metric- and the case of a Fano manifold together with a
-divisor $D$ proportional to the anticanonical class -the limit of the rescaled
-metric is the Tian-Yau metric. 
-\smallskip
-
-On the other hand, there has been increasing interest in the understanding of
-Kähler-Einstein metrics on singular spaces. Perhaps one of the first result in
-this direction is due to S. Kobayashi (construction of orbifold Kähler-Einstein
-metrics), while a definitive existence result for a large class of singularities
-was obtained by Eyssidieux-Guedj-Zeriahi by combining Yau's technique with S.
-Kolodziej's $\mathcal C^0$ estimates. Recently Li-Tian-Wang extended
-Chen-Donaldson-Sun’s solution of the Yau-Tian-Donaldson conjecture to general
-$\mathbb Q$-Fano varieties. Thus, we now have several sources/motivations for
-studying singular Kähler-Einstein metrics on normal varieties.
-
-For applications it is desirable to have control of the geometry of these
-metrics near the singularities, but so far little is known in general. The
-continuity of their potential has only been established very recently (beginning
-of 2024) by Y.-W- Luke and Y.-J. Choi. Beyond that, the main progress in this
-direction is due to Hein-Sun, who showed that near a large class of smoothable
-isolated singularities that are locally isomorphic to a Calabi-Yau cone, the
-singular Calabi-Yau metric must be asymptotic in a strong sense to the
-Calabi-Yau cone metric. Recently an analogous result was shown by Datar-Fu-Song
-in the case of isolated log canonical singularities using the bounded geometry
-method, and precise asymptotics were obtained shortly after by Fu-Hein-Jiang.
-Important contributions in direct connection with these topics are due to S.-K.
-Chiu,T. Delcroix, H.-J. Hein, C. Li, Y. Li, S. Sun, G. Székelyhidi, V. Tosatti
-and K. Zhang.
 
 
-\subsubsection{Complex hyperbolicity}
+\section{Preliminary list of proposed participants}
 
-The Green-Griffiths conjecture (concerning the Zariski closure of holomorphic
+Below is a preliminary list of 55 people (including organizers) we would like to
-entire curves or more generally, of families of holomorphic disks on varieties
+invite\footnote{We list colleagues as ``young'' if they have no tenured job, or
-of general type) continues to keep busy many complex geometers. Probably the
+if their tenure is less than about three years old.}.  About half of them have
-most complete result in this field is due to A. Bloch (more than 100 years ago),
+not attended this workshop before.  The list meets or exceeds the quota on
-who -in modern language- showed that the Zariski closure of a map $\varphi:
+diversity and regionality laid out in the ``Proposal Guidelines for Workshops''.
-\mathbb C \to A$ to a complex tori $A$ is the translate of a sub-tori. A decade
-ago, K.~Yamanoi established the Green-Griffiths conjecture for projective
-manifolds general type, which admit a generically finite map into an Abelian
-variety. This represents a very nice generalization of Bloch's theorem.
 
-In the last couple of years the field is taking a very interesting direction, by
+{\small
-combining techniques from Hodge theory with the familiar Nevanlinna theory and
+\begin{longtable}[c]{lccccccc}
-jet differentials, cf. the articles by D. Brotbek, Y. Deng, Y. Brunebarbe, B.
-Cadorel and A. Javanpeykar.
 
-Using recent advances in the theory of harmonic maps (due to
+\rowcolor{lightgray} \textbf{Name} & \textbf{Location} & \textbf{German} & \textbf{Young} & \textbf{Woman} & \textbf{New to workshop} \\\hline \endhead
-Daskalopoulos-Mese), Y. Deng and K. Yamanoi were able to confirm the
-Green-Griffiths conjecture for manifolds whose fundamental group admits a
-representation having certain natural properties (echoing the case of curves of
-genus at least two). 
-
-Techniques from birational geometry, in connection with the work of F.~Campana
-are also present in the field via the -long awaited- work of E. Rousseau and its
-collaborators. 
-
-
-\subsubsection{Complex hyperbolicity. Mark II}
-
-The 1979 Green-Griffiths-Lang conjecture asserts that every complex-projective
-variety $X$ of general type contains a proper subvariety $Y \subsetneq X$, such
-that every non-constant entire holomorphic curve $\mathbb C \to X$ takes its
-values in $Y$.  Its beginnings date back to 1926, when André Bloch showed that
-the Zariski closure of entire holomorphic curve $\varphi: \mathbb C \to A$ to a
-complex torus $A$ is the translate of a sub-torus. Today, the conjecture still
-drives much of the research in complex geometry. We highlight several advances
-that will be relevant for our workshop.
-
-\paragraph{Hypersurfaces in projective space}
-
-A remarkable paper of Bérczi and Kirwan, \cite{MR4688701} published in September
-last year, establishes hyperbolicity and proves the Green-Griffiths-Lang for
-generic hypersurfaces of the projective space, $X \subsetneq \mathbb P^n$,
-provided that the degree of $X$ is larger than an explicit polynomial in $n$.
-These are significant improvements of earlier degree bounds, which involve
-non-polynomial bounds of order $(\sqrt{n} \log n)^n$ or worse.  The proof builds
-on a strategy of Diverio-Merker-Rousseau and combines non-reductive geometric
-invariant theory with the ``Grassmannian techniques'' of Riedl-Yang.  A very
-recent preprint of Cadorel simplifies the proof Bérczi-Kirwan substantially, but
-still needs to undergo peer review, \cite{arXiv:2406.19003}.
-
-
-\paragraph{Hyperbolicity and representations of fundamental groups}
-
-Using recent advances in the theory of harmonic maps (due to
-Daskalopoulos-Mese), Y. Deng and K. Yamanoi were able to confirm the
-Green-Griffiths conjecture for manifolds whose fundamental group admits a
-representation having certain natural properties (echoing the case of curves of
-genus at least two). 
-
-
-\paragraph{Material collections}
-
-
-
-In the last couple of years the field is taking a very interesting direction, by
-combining techniques from Hodge theory with the familiar Nevanlinna theory and
-jet differentials, cf. the articles by D. Brotbek, Y. Deng, Y. Brunebarbe, B.
-Cadorel and A. Javanpeykar.
 
+di Nezza, Eleonora&Sorbonne&&&1 \\
+Paun, Mihai&Bayreuth&1&& \\
+Kebekus, Stefan&Freiburg&1&& \\
+Schreieder, Stefan&Hannover&1&& \\
+&&&& \\
+Arapura, Donu&Purdue&&&&1 \\
+Bakker, Ben&Chicago&&&& \\
+Bérczi, Gergely&Aarhus&&&&1 \\
+Biquard, Olivier&Sorbonne&&&&1 \\
+Boucksom, Sébastien&Paris&&&& \\
+Braun, Lukas&Innsbruck&1&1&& \\
+Brotbek, Damian&Nancy&&&&1 \\
+Brunebarbe, Yohan&Bordeaux&&&& \\
+Cadorel, Benoît&Nancy&&&& \\
+Chiu, Shih-Kai&Vanderbilt&&1&&1 \\
+Conlon, Ronan&Dallas&&&&1 \\
+Delcroix, Thibault&Montpellier&&&& \\
+Deng, Ya&Nancy&&&& \\
+Dutta, Yajnaseni&Leiden&&&1&1 \\
+Engel, Phil&Bonn&1&1&&1 \\
+Eyssidieux, Phillippe&Grenoble&&&& \\
+Floris, Enrica&Poitiers&&&1& \\
+Friedman, Robert&Columbia&&&&1 \\
+Gachet, Cécile&Bochum&1&1&1&1 \\
+Graf, Patrick&Bayreuth&1&&& \\
+Greb, Daniel&Essen&1&&& \\
+Guedj, Vincent&Toulouse&&&& \\
+Guenancia, Henri&Toulouse&&&& \\
+Hausel, Tamas&IST Austria&&&&1 \\
+Hein, Hans-Joachim&Münster&1&&& \\
+Höring, Andreas&Nice&&&& \\
+Hoskins, Victoria&Nijmegen&&&1&1 \\
+Hwang, Jun-Muk&Daejon, Korea&&&& \\
+Javanpeykar, Arian&Nijmegen&&&& \\
+Kirwan, Frances&Oxford&&&1&1 \\
+Klingler, Bruno&Berlin&1&&& \\
+Lehn, Christian&Bochum&1&&& \\
+Li, Chi&Purdue&&&& \\
+Llosa Isenrich, Claudio&Karlsruhe&1&&&1 \\
+Mauri, Mirko&Paris&&&& \\
+Maxim, Laurenţiu&Wisconsin, Madison&&&&1 \\
+Mustață, Mircea&Ann Arbor&&&& \\
+Park, Sung Gi&Harvard&&1&&1 \\
+Peternell, Thomas&Bayreuth/Hannover&1&&& \\
+Pieropan, Marta&Utrecht&&&1&1 \\
+Popa, Mihnea&Harvard&&&& \\
+Pozzetti, Beatrice&Heidelberg&1&&1&1 \\
+Py, Pierre&Strasbourg&&&&1 \\
+Rousseau, Erwan&Brest&&&& \\
+Schnell, Christian&Stony Brook&&&& \\
+Spelta, Irene&Berlin&1&&1&1 \\
+Stenger, Isabel&Hannover&1&1&1&1 \\
+Sun, Song&Berkely&&&&1 \\
+Székelyhidi, Gabor&Northwestern&&&&1 \\
+Wang, Botong&Wisconsin&&&&1 \\
+Wang, Julie Tzu-Yueh&Taiwan&&&1&1 \\
+Xie, Zhixin&Nancy&&1&1&1
+\end{longtable}
+} % \scriptsize
 
 
 \bibstyle{alpha}

general.bib

@@ -1,3 +1,233 @@
+@Article{zbMATH07863260,
+ Author = {Li, Yang and Tosatti, Valentino},
+ Title = {Special {K{\"a}hler} geometry and holomorphic {Lagrangian} fibrations},
+ FJournal = {Comptes Rendus. Math{\'e}matique. Acad{\'e}mie des Sciences, Paris},
+ Journal = {C. R., Math., Acad. Sci. Paris},
+ ISSN = {1631-073X},
+ Volume = {362},
+ Number = {S1},
+ Pages = {171--196},
+ Year = {2024},
+ Language = {English},
+ DOI = {10.5802/crmath.629},
+ Keywords = {14Jxx,53Cxx,32Qxx},
+ zbMATH = {7863260}
+}
+
+@misc{arXiv:2207.03283,
+      title={Hyperbolicity in presence of a large local system}, 
+      author={Yohan Brunebarbe},
+      month={July},
+      year={2022},
+      note={Preprint \href{https://arxiv.org/abs/2207.03283}{arXiv:2207.03283}},
+      archivePrefix={arXiv},
+      primaryClass={math.AG},
+      url={https://arxiv.org/abs/2207.03283}, 
+}
+
+@misc{arXiv:2305.09613,
+      title={The relative {G}reen-{G}riffiths-{L}ang conjecture for families of varieties of maximal {A}lbanese dimension}, 
+      author={Yohan Brunebarbe},
+      month={May},
+      year={2023},
+      note={Preprint \href{https://arxiv.org/abs/2305.09613}{arXiv:2305.09613}},
+      archivePrefix={arXiv},
+      primaryClass={math.AG},
+      url={https://arxiv.org/abs/2305.09613}, 
+}
+
+@misc{arXiv:2007.12957,
+      title={Arakelov-{N}evanlinna inequalities for variations of {H}odge structures and applications}, 
+      author={Damian Brotbek and Yohan Brunebarbe},
+      month={July},
+      year={2020},
+      note={Preprint \href{https://arxiv.org/abs/2007.12957}{arXiv:2007.12957}},
+      archivePrefix={arXiv},
+      primaryClass={math.AG},
+      url={https://arxiv.org/abs/2007.12957}, 
+}
+
+@misc{arXiv:2112.13961,
+      title={Infinite energy maps and rigidity}, 
+      author={Daskalopoulos, Georgios and Mese, Chikako},
+      month={December},
+      year={2021},
+      note={Preprint \href{https://arxiv.org/abs/2112.13961}{arXiv:2112.13961}},
+      url={https://arxiv.org/abs/2112.13961}
+}
+
+@Article{zbMATH07858206,
+ Author = {Conlon, Ronan J. and Hein, Hans-Joachim},
+ Title = {Classification of asymptotically conical {Calabi}-{Yau} manifolds},
+ FJournal = {Duke Mathematical Journal},
+ Journal = {Duke Math. J.},
+ ISSN = {0012-7094},
+ Volume = {173},
+ Number = {5},
+ Pages = {947--1015},
+ Year = {2024},
+ Language = {English},
+ DOI = {10.1215/00127094-2023-0030},
+ Keywords = {53C25,14J32},
+ zbMATH = {7858206}
+}
+
+@Article{zbMATH07810677,
+ Author = {Chiu, Shih-Kai and Sz{\'e}kelyhidi, G{\'a}bor},
+ Title = {Higher regularity for singular {K{\"a}hler}-{Einstein} metrics},
+ FJournal = {Duke Mathematical Journal},
+ Journal = {Duke Math. J.},
+ ISSN = {0012-7094},
+ Volume = {172},
+ Number = {18},
+ Pages = {3521--3558},
+ Year = {2023},
+ Language = {English},
+ DOI = {10.1215/00127094-2022-0107},
+ Keywords = {32Q20,32Q25,53C25},
+ URL = {projecteuclid.org/journals/duke-mathematical-journal/volume-172/issue-18/Higher-regularity-for-singular-K%c3%a4hlerEinstein-metrics/10.1215/00127094-2022-0107.full},
+ zbMATH = {7810677}
+}
+
+@misc{arXiv:2407.01150,
+      title={Degenerating conic {K}ähler-{E}instein metrics to the normal cone}, 
+      author={Biquard, Olivier and Guenancia, Henri},
+      note={Preprint \href{https://arxiv.org/abs/2407.01150}{arXiv:2407.01150}},
+      year={2024},
+      month={July},
+      url={https://arxiv.org/abs/2407.01150},
+}
+
+@Article{zbMATH07782497,
+ Author = {Fu, Xin and Hein, Hans-Joachim and Jiang, Xumin},
+ Title = {Asymptotics of {K{\"a}hler}-{Einstein} metrics on complex hyperbolic cusps},
+ FJournal = {Calculus of Variations and Partial Differential Equations},
+ Journal = {Calc. Var. Partial Differ. Equ.},
+ ISSN = {0944-2669},
+ Volume = {63},
+ Number = {1},
+ Pages = {34},
+ Note = {Id/No 6},
+ Year = {2024},
+ Language = {English},
+ DOI = {10.1007/s00526-023-02613-4},
+ Keywords = {32Q20,35J96,53C55},
+ zbMATH = {7782497},
+ Zbl = {1535.32023}
+}
+
+@Article{zbMATH07669617,
+ Author = {Datar, Ved and Fu, Xin and Song, Jian},
+ Title = {K{\"a}hler-{Einstein} metrics near an isolated log-canonical singularity},
+ FJournal = {Journal f{\"u}r die Reine und Angewandte Mathematik},
+ Journal = {J. Reine Angew. Math.},
+ ISSN = {0075-4102},
+ Volume = {797},
+ Pages = {79--116},
+ Year = {2023},
+ Language = {English},
+ DOI = {10.1515/crelle-2022-0095},
+ Keywords = {83C75,53C21,32Q20,03C80,35B35,83C30},
+ zbMATH = {7669617},
+ Zbl = {1521.83164}
+}
+
+@Article{zbMATH06827885,
+ Author = {Hein, Hans-Joachim and Sun, Song},
+ Title = {Calabi-{Yau} manifolds with isolated conical singularities},
+ FJournal = {Publications Math{\'e}matiques},
+ Journal = {Publ. Math., Inst. Hautes {\'E}tud. Sci.},
+ ISSN = {0073-8301},
+ Volume = {126},
+ Pages = {73--130},
+ Year = {2017},
+ Language = {English},
+ DOI = {10.1007/s10240-017-0092-1},
+ Keywords = {32Q25,32Q20,14J32},
+ URL = {www.numdam.org/articles/10.1007/s10240-017-0092-1/},
+ zbMATH = {6827885},
+ Zbl = {1397.32009}
+}
+
+@misc{arXiv:2401.03935,
+      title={Continuity of solutions to complex {M}onge-{A}mpère equations on compact {K}ähler spaces}, 
+      author={Ye-Won Luke Cho and Young-Jun Choi},
+      month={January},
+      year={2024},
+      note={Preprint \href{https://arxiv.org/abs/2401.03935}{arXiv:2401.03935}},
+      archivePrefix={arXiv},
+      primaryClass={math.DG},
+      url={https://arxiv.org/abs/2401.03935}, 
+}
+
+@Article{zbMATH07597119,
+ Author = {Li, Chi and Tian, Gang and Wang, Feng},
+ Title = {The uniform version of {Yau}-{Tian}-{Donaldson} conjecture for singular {Fano} varieties},
+ FJournal = {Peking Mathematical Journal},
+ Journal = {Peking Math. J.},
+ ISSN = {2096-6075},
+ Volume = {5},
+ Number = {2},
+ Pages = {383--426},
+ Year = {2022},
+ Language = {English},
+ DOI = {10.1007/s42543-021-00039-5},
+ Keywords = {32Q20,32Q26,14J45},
+ zbMATH = {7597119},
+ Zbl = {1504.32068}
+}
+
+@Article{zbMATH07382001,
+ Author = {Li, Chi and Tian, Gang and Wang, Feng},
+ Title = {On the {Yau}-{Tian}-{Donaldson} conjecture for singular {Fano} varieties},
+ FJournal = {Communications on Pure and Applied Mathematics},
+ Journal = {Commun. Pure Appl. Math.},
+ ISSN = {0010-3640},
+ Volume = {74},
+ Number = {8},
+ Pages = {1748--1800},
+ Year = {2021},
+ Language = {English},
+ DOI = {10.1002/cpa.21936},
+ Keywords = {32Q20,14J45,53C55},
+ zbMATH = {7382001},
+ Zbl = {1484.32041}
+}
+
+@Article{zbMATH05859416,
+ Author = {Eyssidieux, Philippe and Guedj, Vincent and Zeriahi, Ahmed},
+ Title = {Singular {K{\"a}hler}-{Einstein} metrics},
+ FJournal = {Journal of the American Mathematical Society},
+ Journal = {J. Am. Math. Soc.},
+ ISSN = {0894-0347},
+ Volume = {22},
+ Number = {3},
+ Pages = {607--639},
+ Year = {2009},
+ Language = {English},
+ DOI = {10.1090/S0894-0347-09-00629-8},
+ Keywords = {32W20,32Q20,32J27,14J17},
+ zbMATH = {5859416},
+ Zbl = {1215.32017}
+}
+
+@Article{zbMATH07615186,
+ Author = {Biquard, Olivier and Guenancia, Henri},
+ Title = {Degenerating {K{\"a}hler}-{Einstein} cones, locally symmetric cusps, and the {Tian}-{Yau} metric},
+ FJournal = {Inventiones Mathematicae},
+ Journal = {Invent. Math.},
+ ISSN = {0020-9910},
+ Volume = {230},
+ Number = {3},
+ Pages = {1101--1163},
+ Year = {2022},
+ Language = {English},
+ DOI = {10.1007/s00222-022-01138-5},
+ Keywords = {32Q20,53C55,35J99},
+ zbMATH = {7615186},
+ Zbl = {1510.32057}
+}
+
 @Article{zbMATH07790946,
  Author = {Llosa Isenrich, Claudio and Py, Pierre},
  Title = {Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices},
@@ -17,9 +247,11 @@
 
 
 @misc{arXiv:2310.14131,
-      title={Hodge-theoretic variants of the Hopf and Singer Conjectures}, 
+      title={Hodge-theoretic variants of the {H}opf and {S}inger {C}onjectures}, 
       author={Donu Arapura and Laurentiu Maxim and Botong Wang},
-      year={2024},
+      note={Preprint \href{https://arxiv.org/abs/2310.14131}{arXiv:2310.14131}},
+      month={October},
+      year={2023},
       eprint={2310.14131},
       archivePrefix={arXiv},
       primaryClass={math.AG},
@@ -27,40 +259,44 @@
 }
 
 @misc{arXiv:2303.05364,
-      title={Hodge theory and Lagrangian fibrations on holomorphic symplectic manifolds}, 
+      title={Hodge theory and {L}agrangian fibrations on holomorphic symplectic manifolds}, 
       author={Christian Schnell},
+      month={March},
       year={2023},
-      eprint={2303.05364},
+      note={Preprint \href{https://arxiv.org/abs/2303.05364}{arXiv:2303.05364}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2303.05364}, 
 }
 
 @misc{arXiv:2209.05429,
-      title={$P=W$ via $H_2$}, 
+      title={{$P=W$} via {$H_2$}}, 
       author={Tamas Hausel and Anton Mellit and Alexandre Minets and Olivier Schiffmann},
+      month={September},
       year={2022},
-      eprint={2209.05429},
+      note={Preprint \href{https://arxiv.org/abs/2209.05429}{arXiv:2209.05429}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2209.05429}, 
 }
 
 @misc{arXiv:2209.02568,
-      title={The $P=W$ conjecture for $\mathrm{GL}_n$}, 
+      title={The {$P=W$} conjecture for {$\mathrm{GL}_n$}}, 
       author={Davesh Maulik and Junliang Shen},
-      year={2024},
+      month={September},
-      eprint={2209.02568},
+      year={2022},
+      note={Preprint \href{https://arxiv.org/abs/2209.02568}{arXiv:2209.02568}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2209.02568}, 
 }
 
 @misc{arXiv:2311.08977,
-      title={A Hodge-theoretic proof of Hwang's theorem on base manifolds of Lagrangian fibrations}, 
+      title={A {H}odge-theoretic proof of {H}wang's theorem on base manifolds of {L}agrangian fibrations}, 
       author={Benjamin Bakker and Christian Schnell},
+      month={November},
       year={2023},
-      eprint={2311.08977},
+      note={Preprint \href{https://arxiv.org/abs/2311.08977}{arXiv:2311.08977}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2311.08977}, 
@@ -71,12 +307,30 @@
       author={Christian Schnell and Ruijie Yang},
       month={September},
       year={2023},
-      eprint={2309.16763},
+      note={Preprint \href{https://arxiv.org/abs/2309.16763}{arXiv:2309.16763}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2309.16763}, 
 }
 
+@article {MR4044463,
+    AUTHOR = {Musta\c t\u a, Mircea and Popa, Mihnea},
+     TITLE = {Hodge ideals},
+   JOURNAL = {Mem. Amer. Math. Soc.},
+  FJOURNAL = {Memoirs of the American Mathematical Society},
+    VOLUME = {262},
+      YEAR = {2019},
+    NUMBER = {1268},
+     PAGES = {v+80},
+      ISSN = {0065-9266,1947-6221},
+      ISBN = {978-1-4704-3781-7; 978-1-4704-5509-5},
+   MRCLASS = {14D07 (14F17 14J17 32S25)},
+  MRNUMBER = {4044463},
+MRREVIEWER = {Matthias\ Wendt},
+       DOI = {10.1090/memo/1268},
+       URL = {https://doi.org/10.1090/memo/1268},
+}
+
 @article {MR4081135,
     AUTHOR = {Mustaţă, Mircea and Popa, Mihnea},
      TITLE = {Hodge filtration, minimal exponent, and local vanishing},
@@ -95,11 +349,11 @@ MRREVIEWER = {Zhi\ Jiang},
 }
 
 @misc{arXiv:2406.19003,
-      title={Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials}, 
+      title={Hyperbolicity of generic hypersurfaces of polynomial degree via {G}reen-{G}riffiths jet differentials}, 
       author={Benoit Cadorel},
-      year={2024},
       month={June},
-      eprint={2406.19003},
+      year={2024},
+      note={Preprint \href{https://arxiv.org/abs/2406.19003}{arXiv:2406.19003}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2406.19003},