From f05be190043e2241e492159f565eead345998843 Mon Sep 17 00:00:00 2001 From: Stefan Kebekus Date: Wed, 24 Jul 2024 15:46:53 +0200 Subject: [PATCH] Add Stefan's comments --- .gitignore | 1 + MFO26.tex | 49 ++++++++++++++++++++++++++++++++++--------------- 2 files changed, 35 insertions(+), 15 deletions(-) diff --git a/.gitignore b/.gitignore index e162a11..0597b27 100644 --- a/.gitignore +++ b/.gitignore @@ -16,3 +16,4 @@ *.synctex(busy) *.synctex.gz *.toc +*.xlsx \ No newline at end of file diff --git a/MFO26.tex b/MFO26.tex index 207641c..2edc70b 100644 --- a/MFO26.tex +++ b/MFO26.tex @@ -55,7 +55,7 @@ \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} @@ -97,12 +97,35 @@ Komplexe Analysis --- Differential and Metric Methods in the Theory of Kähler S \section{Abstract} -Complex Analysis is a very active branch of mathematics with applications in 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. -%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. +Complex Analysis is a very active branch of mathematics with applications in +many other fields. The proposed workshop presents recent results in complex +analysis and especially the analytic and algebraic study of Kähler spaces, and +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} @@ -121,17 +144,14 @@ Secondary & 14 &--& Algebraic geometry \\ The proposed workshop presents recent results in Complex Geometry and surveys relations to other fields. For 2026, we would like to emphasize the fields -described below. -Each relates to complex analysis differently. -Each has seen substantial progress recently, producing results that will be of importance for years to come. -%The bullet items list some of the latest developments that have attracted our attention. +described below. Each relates to complex analysis differently. Each has seen +substantial progress recently, producing results that will be of importance for +years to come. -%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 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 for informal discussions. -%After so many months of the pandemic, this will be more than welcome! \subsection{Canonical Metrics and Hyperbolicity} @@ -247,9 +267,8 @@ curves. 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, commutative algebra, and -the topology of algebraic varieties. The following topics in this area will -particularly interest our workshop. +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}