Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Surface Bundles
No full textThis workshop brought together specialists in algebraic topology, low dimensional topology, geometric group theory, algebraic geometry and neighboring fields. It provided a good overview of the current developments, and highlighted significant progress in the field. Furthermore it showed an increasing amount of interaction between specialists in different fields who are interested in the different facets of the rich theory of surface bundles
Graph Theory
No full textThis workshop focused on recent developments in graph theory. These included in particular recent breakthroughs on nowhere-zero flows in graphs, width parameters, applications of graph sparsity in algorithms, and matroid structure results
Statistics for Shape and Geometric Features
No full textThe constant emergence of novel technologies result in novel data generating devices and mechanisms that lead to a prevalence of highly complex data. To analyze such data, novel statistical methodologies need to be developed. This workshop addressed challenges that arise in the theoretical analyses of procedures in which geometry, shape and topology play central roles. The theoretical ideas involved here intersect deeply with a wide variety of fields, including mathematical statistics, probability theory, computational topology, and computational and differential geometry. The workshop brought together scholars with different perspectives, with the goal of facilitating cross-pollination to spur the development of new ideas, new analytical approaches, and new methods in geometric and shape statistics
On densities of lattice arrangements intersecting every i-dimensional affine subspace
No full textResearch in Pairs 2014In 1978, Makai Jr. established a remarkable connection between the volume-product of a convex body, its maximal lattice packing density and the minimal density of a lattice arrangement of its polar body intersecting every affine hyperplane. Consequently, he formulated a conjecture that can be seen as a dual analog of Minkowski’s fundamental theorem, and which is strongly linked to the well-known Mahlerconjecture. Based on the covering minima of Kannan & Lovász and a problem posed by Fejes Tóth, we arrange Makai Jr.’s conjecture into a wider context and investigate densities of lattice arrangements of convex bodies intersecting every i-dimensional affine subspace. Then it becomes natural also to formulate and study a dual analog to Minkowski’s second fundamental theorem. As our main results, we derive meaningful asymptotic lower bounds for the densities of such arrangements, and furthermore, we solve the problems exactly for the special, yet important, class of unconditional convex bodies
Analytic Structure in Fibers
No full textResearch in Pairs 2015Let be the open unit ball of a complex Banach space , and let and be, respectively, the algebra of bounded holomorphic functions on and the subalgebra of uniformly continuous holomorphic functions on . In this paper we study the analytic structure of fibers in the spectrum of these two algebras. For the case of , we prove that the fiber in over any point of the distinguished boundary of the closed unit ball of contains an analytic copy of . In the case of we prove that if there exists a polynomial whose restriction to the open unit ball of is not weakly continuous at some point, then the fiber over every point of the open unit ball of the bidual contains an analytic copy of
New Developments in Functional and Highly Multivariate Statistical Methodology
No full textThe central focus of the workshop was on recent developments in statistical techniques for highly multivariate data and functional data. The programme delivered talks on state-of-the-art research in the area, with a number of talks on highly-dimensional multivariate settings as well as talks dealing with functional data. The talks were followed by lively discussions on how to tackle difficult issues in the statistical methodology for such complex data
Large Scale Stochastic Dynamics
No full textThe goal of this workshop was to explore the recent advances in the mathematical understanding of the macroscopic properties which emerge on large space-time scales from interacting microscopic particle systems. There were 53 participants, including 4 postdocs and graduate students, working in diverse intertwining areas of probability and statistical mechanics. During the meeting, 24 talks of 50 minutes were scheduled and an evening session was organised with 10 more short talks of 10 minutes, mostly by younger participants. These talks addressed the following topics: hydrodynamic limits and hydrodynamic fluctuations with a special emphasis on KPZ fluctuations, scaling limits in percolation and random walks, approach to equilibrium in reversible systems with a strong focus on kinetically constrained dynamics
Visual analysis of Spanish male mortality
No full textDie statistische Visualisierung benutzt graphische Methoden um Erkenntnisse aus Daten zu gewinnen. Wir zeigen wie mit dem Verfahren der Hauptkomponentenanalyse die Sterblichkeit in Spanien im Laufe der letzten hundert Jahre analysiert werden kann. Diese Datenzerlegung zeigt sowohl erwartete geschichtliche Ereignisse auf, als auch einige, teilweise überraschende Entwicklungen der Sterblichkeit im Laufe der Zeit
Mini-Workshop: Fast Solvers for Highly Oscillatory Problems
No full textThe efficient numerical solution of highly oscillatory problems is one of the grand challenges of Applied Mathematics with diverse applications across the natural sciences and engineering. This workshop brings together experts in domain based methods and integral equation methods to share novel ideas and to discuss challenges on the way to developing efficient solvers at high frequencies
Asymptotic Phenomena in Local Algebra and Singularity Theory
No full textThe goal of this workshop was to highlight, and further, the interactions between local algebra and singularity theory. The timing was serendipitous for both subjects have witnessed tremendous progress recently, much of which was reported at the workshop