2021, Hamenstädt, Ursula, Lang, Urs, Weinkove, Ben

The field of classical differential geometry has expanded enormously over the last several decades, helped by the development of tools from neighboring fields such as partial differential equations, complex analysis and geometric topology. In the spirit of the previous meetings in the series, this meeting will bring together researchers from apparently separate subfields of differential geometry, but whose work is linked by common themes. In particular, this meeting will emphasize intrinsic geometric questions motivated by the classification and rigidity of global geometric structures and the interaction of curvature with the underlying geometry and topology.

2020, Drutu, Cornelia, Kramer, Linus, Rémy, Bertrand

The conference focused on the use of geometric methods to study infinite groups and the interplay of group theory with other areas. One of the central techniques in geometric group theory is to study infinite discrete groups by their actions on nice, suitable spaces. These spaces often carry an interesting large-scale geometry, such as non-positive curvature or hyperbolicity in the sense of Gromov, or are equipped with rich geometric or combinatorial structure. From these actions one can investigate structural properties of the groups. This connection has become very prominent during the last years. In this context non-discrete topological groups, such as profinite groups or locally compact groups appear quite naturally. Likewise, analytic methods and operator theory play an increasing role in the area.

2020, Herzog, Roland, Steidl, Gabriele

The goal of the mini-workshop was to study the geometry, algorithms and applications of unconstrained and constrained optimization problems posed on Riemannian manifolds. Focus topics included the geometry of particular manifolds, the formulation and analysis of a number of application problems, as well as novel algorithms and their implementation.

2023, Nüst, Daniel, Hauschke, Christian, Coordts, Anette, Yücel, Gazi

Die Metadatenallmende ist ein wichtiger Baustein für den Wandel hin zu einem diversen Open-Access-Ökosystem. Nur mit offenen und hochwertigen Metadaten, die mindestens die gleiche oder sogar höhere Qualität und Abdeckung als die Metadaten-Silos etablierter kommerzieller Verlage erreichen, können unabhängige Zeitschriften auf Augenhöhe Themen wie Auffindbarkeit und faire Evaluation von Forschenden angehen. Wir stellen einen Arbeitsablauf und Werkzeuge vor, die eine Professionalisierung der Metadatenprozesse von unabhängigen, scholar-led OA-Journals unterstützen. Diese Journals können damit ihre Sichtbarkeit im Wissenschaftssystem und ihre Bedeutung als Publikationsort erhöhen. Dazu wird die global verbreitete Free and Open Source Software (FOSS) Open Journal Systems (OJS) um Funktionen erweitert, die a) Eingabe, Kuratierung und Anreicherung von artikelbezogenen Metadaten durch Autor:innen und Editor:innen und b) den Export dieser Metadaten an offene Datenquellen wie z. B. Wikidata ermöglichen. Diese Erweiterung wird durch OJS-Plugins und auch Anpassung der OJS-Kernsoftware in den folgenden Anwendungsfällen umgesetzt: Erstens ermöglicht die Integration von validierten persistenten Identifikatoren (PIDs) und geographischen Metadaten als Teil der Publikationsmetadaten eine bessere Auffindbarkeit und von Artikeln aus Open-Access-Zeitschriften. PIDs und Geometadaten stellen Verbindungen zu anderen Publikationen, akademischen Events, physischen Proben und wissenschaftlichen Instrumenten her und verknüpfen so verwandte Artikel über Zeitschriften und Wissenschaftsdisziplinen hinweg. Auf Basis dieser Metadaten werden zum Beispiel eine Suchplattform realisiert, die wissenschaftliche Artikel über Disziplingrenzen und Publikationsplatformen hinweg als offene Daten interaktiv auf einer Karte darstellt, und semantisch bedeutsame Links in Artikeln und ihren Landing Pages eingefügt. Zweitens werden Zitationsmetadaten während des Einreichungs- und Begutachtungsprozesses strukturiert erfasst und frei in standardisierten Formaten veröffentlicht. Durch die innovative und benutzerfreundliche Metadatenerfassung im Zuge des wissenschaftlichen Ver­öffentlichungsprozesses können Open-Access-Artikel in transparenten zitationsbasierten Evaluationsmetriken verwendet werden. Diese Neuerungen unterstützen eine offene Publikationskultur und -praxis. In diesem Beitrag berichten wir vom aktuellen Arbeitsstand zu den Anwendungsfällen und beschreiben eine Vision für eine neuartige verteilte Erfassung und Veröffentlichung offener Metadaten.

2021, Barthe, Franck, Ludwig, Monika

The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of algorithms in computer science. The purpose of this meeting was to bring together researchers from the analytic, geometric and probabilistic groups who have contributed to these developments.

2020, Kohn, Robert V., Toro, Tatiana, Wickramasekera, Neshan

Calculus of Variations touches several interrelated areas. In this workshop we covered several topics, such as minimal submanifolds, mean curvature and related flows, free boundary problems, variational models of interacting dislocations, defects in physical systems, phase transitions, etc.

2021, Grushevsky, Samuel, Möller, Martin

The recent developments in hyperbolic geometry and flat geometry in real dimension $2$ formed the core of the workshop, with an emphasis on enumerative aspects. A particularly important role in this regard was played by intersection-theoretic techniques on $\overline{\mathcal{M}}_{g,n}$, the geometry of the strata of differentials, the geometry of Hurwitz spaces, topological recursion techniques, and large genus asymptotics. The workshop included an exploration of relations with similar problems in complex dimension $2$, tropical techniques for enumerative problems, and relations to mathematical physics.

2021, Chirilus-Bruckner, Martina, Kühn, Christian, Rademacher, Jens

The dynamics of waves and patterns play a significant role in the sciences, especially in fluid mechanics, material science, neuroscience and ecology. The mathematical treatment interconnects several areas, ranging from evolution equations and functional analysis to dynamical systems, geometry, topology, and stochastic as well as numerical analysis. This workshop has specifically focussed on dynamic stability on extended domains, bifurcations of waves and patterns, effects of stochastic driving, and spatio-temporal inhomogenities. During the workshop, multiple new directions, collaborations, and very interesting scientific conversations arose across the entire field.

2020, Dümbgen, Lutz, Müller, Klaus-Robert, Samworth, Richard

Theory and application go hand in hand in most areas of statistics. In a world flooded with huge amounts of data waiting to be analyzed, classified and transformed into useful outputs, the designing of fast, robust and stable algorithms has never been as important as it is today. On the other hand, irrespective of whether the focus is put on estimation, prediction, classification or other purposes, it is equally crucial to provide clear guarantees that such algorithms have strong theoretical guarantees. Many statisticians, independently of their original research interests, have become increasingly aware of the importance of the numerical needs faced in numerous applications including gene expression profiling, health care, pattern and speech recognition, data security, marketing personalization, natural language processing, to name just a few. The goal of this workshop is twofold: (a) exchange knowledge on successful algorithmic approaches and discuss some of the existing challenges, and (b) to bring together researchers in statistics and machine learning with the aim of sharing expertise and exploiting possible differences in points of views to obtain a better understanding of some of the common important problems.

2020, Ramassamy, Sanjay, Russkikh, Marianna

The goal of this mini-workshop is to gather specialists of the dimer, Ising and spanning tree models around recent and ongoing progress in two directions. One is understanding the connection to the spectral curve of these models in the cases when the curve has positive genus. The other is the introduction of universal embeddings associated to these models. We aim to use these new tools to progress in the study of scaling limits.