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Stefan Kebekus 2024-07-24 15:46:53 +02:00
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*.synctex(busy) *.synctex(busy)
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*.toc *.toc
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\section{Workshop Title} \section{Workshop Title}
Komplexe Analysis --- Differential and Metric Methods in the Theory of Kähler Spaces Komplexe Analysis --- Differential and Algebraic Methods in the Theory of Kähler Spaces
\section{Proposed Organisers} \section{Proposed Organisers}
@ -97,12 +97,35 @@ Komplexe Analysis --- Differential and Metric Methods in the Theory of Kähler S
\section{Abstract} \section{Abstract}
Complex Analysis is a very active branch of mathematics with applications in many other fields. Complex Analysis is a very active branch of mathematics with applications in
The proposed workshop presents recent results in complex many other fields. The proposed workshop presents recent results in complex
analysis and surveys progress in topics that link the field to other branches of mathematics. analysis and especially the analytic and algebraic study of Kähler spaces, and
%This application highlights differential-geometric methods in the study of singular spaces, the interplay between analytic and algebraic methods, and the relation between complex analysis and Scholze-Clausen's condensed mathematics. surveys progress in topics that link the field to other branches of mathematics.
This application highlights canonical metrics and their limits, hyperbolicity
properties of complex algebraic varieties and the topology and Hodge theory of
Kähler spaces.
%The meeting has always been a venue where confirmed researchers from different backgrounds meet and where young mathematicians are giving their first talks at an international conference. While we are happy to see a growing number of talented, young researchers, we feel that this age group suffers the most from the ongoing COVID crisis and the resulting lack of exchange and interaction. We would therefore like to emphasize the contributions of younger researchers and invite a relatively higher number of them. We are looking forward to welcoming them to Oberwolfach, rediscover the pleasure of meeting in person, and exchange points of view! An important aspect of our workshop are its close ties to other branches of
mathematics. Our aim is to invite a few experts from neighboring fields where we
expect fruitful interactions in the future. For instance, we will include a
small number of geometric group theorists, including Py and Llosa-Isenrich,
that have recently applied methods from complex geometry and Hodge theory to
solve longstanding open problems in geometric group theory.
%This application highlights differential-geometric methods in the study of
%singular spaces, the interplay between analytic and algebraic methods, and the
%relation between complex analysis and Scholze-Clausen's condensed mathematics.
%The meeting has always been a venue where confirmed researchers from different
%backgrounds meet and where young mathematicians are giving their first talks at
%an international conference. While we are happy to see a growing number of
%talented, young researchers, we feel that this age group suffers the most from
%the ongoing COVID crisis and the resulting lack of exchange and interaction.
%We would therefore like to emphasize the contributions of younger researchers
%and invite a relatively higher number of them. We are looking forward to
%welcoming them to Oberwolfach, rediscover the pleasure of meeting in person,
%and exchange points of view!
\section{Mathematics Subject Classification} \section{Mathematics Subject Classification}
@ -121,17 +144,14 @@ Secondary & 14 &--& Algebraic geometry \\
The proposed workshop presents recent results in Complex Geometry and surveys The proposed workshop presents recent results in Complex Geometry and surveys
relations to other fields. For 2026, we would like to emphasize the fields relations to other fields. For 2026, we would like to emphasize the fields
described below. described below. Each relates to complex analysis differently. Each has seen
Each relates to complex analysis differently. substantial progress recently, producing results that will be of importance for
Each has seen substantial progress recently, producing results that will be of importance for years to come. years to come.
%The bullet items list some of the latest developments that have attracted our attention.
%We plan to include at least one broader overview talk for each of the three subjects, as well as more specialized presentations by senior experts and junior researchers.
We will account for new developments that arise between the time of submission We will account for new developments that arise between the time of submission
of this proposal and the time of the workshop. Following good Oberwolfach of this proposal and the time of the workshop. Following good Oberwolfach
tradition, we will keep the number of talks small to provide ample opportunity tradition, we will keep the number of talks small to provide ample opportunity
for informal discussions. for informal discussions.
%After so many months of the pandemic, this will be more than welcome!
\subsection{Canonical Metrics and Hyperbolicity} \subsection{Canonical Metrics and Hyperbolicity}
@ -247,9 +267,8 @@ curves.
Ever since its invention, Hodge theory has been one of the most powerful tools 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 in studying the geometry and topology of Kähler spaces. More recent
developments connect the theory to singularity theory, commutative algebra, and developments connect the theory to singularity theory and commutative algebra.
the topology of algebraic varieties. The following topics in this area will The following topics in this area will particularly interest our workshop.
particularly interest our workshop.
\subsubsection{Singularities and Hodge Ideals} \subsubsection{Singularities and Hodge Ideals}