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

@@ -1,60 +0,0 @@
-Zariski
-holomorphic
-geometers
-Yamanoi
-Brotbek
-Brunebarbe
-Cadorel
-Javanpeykar
-Campana
-hyperbolicity
-subvariety
-Bérczi
-Kirwan
-hypersurfaces
-Diverio-Merker-Rousseau
-Grassmannian
-Riedl-Yang
-Bérczi-Kirwan
-Nezza
-Kebekus
-Mihai
-Păun
-Schreieder
-Kähler
-Saito
-Mustaţă
-Popa
-Schnell
-Bernstein-Sato
-Debarre
-Casalaina-Martin
-Grushevsky
-Riemann-Schottky
-Lefschetz
-Goresky-MacPherson
-Laza
-Calabi-Yau
-fibration
-fibrations
-hyperkähler
-Langrangian
-Bakker
-Shen
-Maulik
-Hausel
-Mellit
-Minets
-Schiffmann
-pushforward
-Maulik-Shen-Yin
-Singer-Hopf
-Hopf
-Arapura
-Sato
-Llosa-Isenrich
-Py
-Goresky
-Schottky
-Calabi
-Yau

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

@@ -1,3 +0,0 @@
-{"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$"}

MFO26.tex

@@ -71,70 +71,69 @@
 
 \subsection{Topology of Kähler spaces: D-modules, perverse sheaves, Hodge modules}
 
-Over the last decade, Saito's theory of Hodge modules has seen spectacular
+Over the last decade, Saito’s theory of Hodge modules has seen spectacular
-applications in birational geometry.  More recent developments connect the
+applications in birational geometry. Over the last few years the theory has been
-theory to singularity theory, commutative algebra, and the topology of algebraic
+further developed and branched out to yield exciting applications to the
-varieties.  The following topics in this area will be of particular interest to
+topology of algebraic varieties, singularity theory and commutative algebra.  
-our workshop.
+The following topics in this area will be of particular interest to our workshop.
-
 
 \subsubsection{Singularities and Hodge ideals}
 
-In a series of influential papers starting with \cite{MR4081135}, Mustaţă and
+Hodge modules are used to define generalizations of well-known ideals of
-Popa used Hodge modules to refine and generalize well-known invariants of
+singularities, such as multiplier ideals from analysis and algebraic geometry.
-singularities, most notably the multiplier ideals used in analysis and algebraic
+This theory has been put forward by Mustata and Popa, an alternative approach
-geometry. An alternative approach towards similar ends was recently suggested in
+was suggested by Schnell and Yang. These generalizations allow to study for
-the preprint \cite{arXiv:2309.16763} of Schnell and Yang.  First applications
+instance Bernstein-Sato polynomials, which are important commutative algebra
-pertain to Bernstein--Sato polynomials and their zero sets; these are important
+invariants of singularities that are typically hard to compute. Geometric
-invariants of singularities originating from commutative algebra that are hard
+applications are given by the study of singularities of Theta divisors of
-to compute.  Schnell and Yang apply their results to conjectures of
+principally polarized abelian varieties, as pursued by Schnell and Yang. 
-Debarre--Casalaina-Martin--Grushevsky concerning the Riemann--Schottky problem
-and the singularities of Theta divisors of principally polarized Abelian
-varieties. 
 
-Very recently, Park and Popa applied perverse sheaves and D-module theory to
+In most recent developments by Park and Popa, related methods have been used to
-improve Goresky--MacPherson's classic Lefschetz theorems in the singular setting.
+improve classical Lefschetz theorems for singular varieties due to Goresky-Mac
-A program put forward by Friedman--Laza aims at understanding the Hodge
+Pherson. Originally, Lefschetz theorems for singular varieties have been proven
-structures of degenerating Calabi--Yau varieties. 
+via stratified Morse theory, while the recent improvements rely on perverse
+sheaves and D-module theory. 
+
+A related program put forward by Friedman and Laza aims at understanding the
+Hodge structures of degenerating Calabi-Yau varieties. This led to the notions
+of higher Du Bois and higher rational singularities which can be understood via
+Hodge modules and will. 
 
 
 \subsubsection{Lagrangian fibrations}
 
-A Lagrangian fibration of a hyperkähler manifold $M$ is a proper holomorphic map
+A Lagrangian fibration of a (not necessarily compact) hyperkaehler manifold $M$
-$f : M \to B$ whose generic fibers are Langrangian. 
+is a proper holomorphic map $f:M\to B$ whose fibres are Langrangian
-
+submanifolds. If $M$ is compact, then a well-known conjecture in the field
-If $M$ is compact, a well-known conjecture in the field predicts that $B$ is
+predicts that $B$ is projective space. This is known if $B$ is smooth by
-projective space.  In case where $B$ is smooth, the conjecture has been
+celebrated work of Hwang. A Hodge theoretic proof of Hwang‘s result has recently
-established more than 16 years ago in a celebrated work of Hwang.  Today, there
+been found by Bakker and Schnell; the case where $B$ is allowed to be singular
-is new insight, as Bakker--Schnell recently found a purely Hodge theoretic proof
+remains open. 
-of Hwang's result, \cite{arXiv:2311.08977}.  There is hope that these methods
-give insight into the singular setting, which remains open to date. 
 
 In the non-compact setting, Lagrangian fibrations have been studied in the
-framework of the so called $P=W$ conjecture, which has recently been proven by
+framework of the so called P=W conjecture, which has recently been proven by
-Maulik--Shen and Hausel--Mellit--Minets--Schiffmann, \cite{arXiv:2209.02568,
+Maulik and Shen for the Hitchin fibration associated to the general linear group
-arXiv:2209.05429}.  In the same setting, Shen--Yin discovered a remarkable
+and curves of arbitrary genus $g\geq 2$. Shen and Yin discovered a remarkable
-symmetry of certain pushforward sheaves and conjectured that more general
+symmetry of certain pushforward sheaves in the case of Lagrangian fibrations
-symmetries exist.  These conjectures have recently been established by Schnell,
+over possibly non-compact bases. Recently, Schnell used Saito‘s theory of Hodge
-\cite{arXiv:2303.05364}, who also proved two conjectures of Maulik--Shen--Yin on
+modules to prove the conjecture of Shen and Yin in full generality.
-the behavior of certain perverse sheaves near singular fibers.
 
 
-\subsubsection{Singer--Hopf conjecture and fundamental groups of Kähler manifolds}
+\subsubsection{Singer-Hopf conjecture and fundamental groups of K\"ahler manifolds}
 
-The Singer--Hopf conjecture asserts that a closed aspherical manifold of real
+The Singer-Hopf conjecture says that a closed aspherical manifold of real
-dimension $2n$ has positive signed Euler characteristic, $(-1)^n \cdot
+dimension $2n$ has positive signed Euler characteristic $(-1)^n\chi(X)\geq 0$.
-\chi(X)\geq 0$. This conjecture goes back to 1931, when Hopf formulated a
+This conjecture goes back to 1931, when Hopf formulated a related version for
-related version for Riemannian manifolds. Recently, Hodge-theoretic refinements
+Riemannian manifolds. Recently, Hodge-theoretic refinements of this conjecture
-of this conjecture for Kähler manifolds have been put forward by
+for K\"ahler manifolds have been put forward by Arapura, Maxim and Wang. Special
-Arapura--Maxim--Wang, \cite{arXiv:2310.14131}. Special cases of these conjecture
+cases of these conjecture have recently been proven, but the statement remains
-have been proven, but the statement remains open in full generality.
+open in full generality.
 
-In a related direction, Llosa-Isenrich--Py found an application of complex
+In a related direction, Llosa-Isenrich and Py found recently an application of
-geometry and Hodge theory to geometric group theory, settling an old question of
+complex geometry and Hodge theory to geometric group theory, thereby settling an
-Brady on finiteness properties of groups, \cite{zbMATH07790946}. As a byproduct,
+old question of of Brady  on finiteness properties of groups. As a byproduct,
 the authors also obtain a proof of the classical Singer conjecture in an
-important special case in the realm of Kähler manifolds.
+important special case in the realm of K\"ahler manifolds.
 
 Our goal in this workshop is to bring together several experts in geometric
 group theory with experts on Hodge theory, and to explore further potential

general.bib

@@ -1,98 +1,3 @@
-@Article{zbMATH07790946,
- Author = {Llosa Isenrich, Claudio and Py, Pierre},
- Title = {Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices},
- FJournal = {Inventiones Mathematicae},
- Journal = {Invent. Math.},
- ISSN = {0020-9910},
- Volume = {235},
- Number = {1},
- Pages = {233--254},
- Year = {2024},
- Language = {English},
- DOI = {10.1007/s00222-023-01223-3},
- Keywords = {20F65,20F67,57M07,32J27},
- zbMATH = {7790946},
- Zbl = {1530.20138}
-}
-
-
-@misc{arXiv:2310.14131,
-      title={Hodge-theoretic variants of the Hopf and Singer Conjectures}, 
-      author={Donu Arapura and Laurentiu Maxim and Botong Wang},
-      year={2024},
-      eprint={2310.14131},
-      archivePrefix={arXiv},
-      primaryClass={math.AG},
-      url={https://arxiv.org/abs/2310.14131}, 
-}
-
-@misc{arXiv:2303.05364,
-      title={Hodge theory and Lagrangian fibrations on holomorphic symplectic manifolds}, 
-      author={Christian Schnell},
-      year={2023},
-      eprint={2303.05364},
-      archivePrefix={arXiv},
-      primaryClass={math.AG},
-      url={https://arxiv.org/abs/2303.05364}, 
-}
-
-@misc{arXiv:2209.05429,
-      title={$P=W$ via $H_2$}, 
-      author={Tamas Hausel and Anton Mellit and Alexandre Minets and Olivier Schiffmann},
-      year={2022},
-      eprint={2209.05429},
-      archivePrefix={arXiv},
-      primaryClass={math.AG},
-      url={https://arxiv.org/abs/2209.05429}, 
-}
-
-@misc{arXiv:2209.02568,
-      title={The $P=W$ conjecture for $\mathrm{GL}_n$}, 
-      author={Davesh Maulik and Junliang Shen},
-      year={2024},
-      eprint={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}, 
-      author={Benjamin Bakker and Christian Schnell},
-      year={2023},
-      eprint={2311.08977},
-      archivePrefix={arXiv},
-      primaryClass={math.AG},
-      url={https://arxiv.org/abs/2311.08977}, 
-}
-
-@misc{arXiv:2309.16763,
-      title={Higher multiplier ideals}, 
-      author={Christian Schnell and Ruijie Yang},
-      month={September},
-      year={2023},
-      eprint={2309.16763},
-      archivePrefix={arXiv},
-      primaryClass={math.AG},
-      url={https://arxiv.org/abs/2309.16763}, 
-}
-
-@article {MR4081135,
-    AUTHOR = {Mustaţă, Mircea and Popa, Mihnea},
-     TITLE = {Hodge filtration, minimal exponent, and local vanishing},
-   JOURNAL = {Invent. Math.},
-  FJOURNAL = {Inventiones Mathematicae},
-    VOLUME = {220},
-      YEAR = {2020},
-    NUMBER = {2},
-     PAGES = {453--478},
-      ISSN = {0020-9910,1432-1297},
-   MRCLASS = {14F10 (14F17 14J17 32S25)},
-  MRNUMBER = {4081135},
-MRREVIEWER = {Zhi\ Jiang},
-       DOI = {10.1007/s00222-019-00933-x},
-       URL = {https://doi.org/10.1007/s00222-019-00933-x},
-}
 
 @misc{arXiv:2406.19003,
       title={Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials},