Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Das Problem der Kugelpackung
No full textWie würdest du Tennisbälle oder Orangen stapeln? Oder allgemeiner formuliert: Wie dicht lassen sich identische 3-dimensionale Objekte überschneidungsfrei anordnen? Das Problem, welches auch Anwendungen in der digitalen Kommunikation hat, hört sich einfach an, ist jedoch für Kugeln in höheren Dimensionen noch immer ungelöst. Sogar die Berechnung guter Näherungslösungen ist für die meisten Dimensionen schwierig
Yet another algorithm for the symmetric eigenvalue problem
No full textResearch in Pairs 2016In this paper we present a new algorithm for solving the symmetric matrix eigenvalue problem that works by first using a Cayley transformation to convert the symmetric matrix into a unitary one and then uses Gragg’s implicitly shifted unitary QR algorithm to solve the resulting unitary eigenvalue problem. We prove that under reasonable assumptions on the symmetric matrix this algorithm is backward stable and also demonstrate that this algorithm is comparable with other well known implementations in terms of both speed and accuracy
Late-Time Behaviour of Israel Particles in a FLRW Spacetime with Λ>0
No full textResearch in Pairs 2016In this paper we study the relativistic Boltzmann equation in a spatially flat FLRW space-time. We consider Israel particles, which are the relativistic counterpart of the Maxwellian particles, and obtain global-in-time existence and the asymptotic behaviour of solutions. The main argument of the paper is to use the energy method of Guo, and we observe that the method can be applied to study small solutions in a cosmological case. It is the first result of this type where a physically well-motivated scattering kernel is considered for the general relativistic Boltzmann equation
Mathematical Imaging and Surface Processing
No full textWithin the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images.
This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains
The Willmore Conjecture
No full textThe Willmore problem studies which torus has the least amount of bending energy. We explain how to think of a torus as a donut-shaped surface and how the intuitive notion of bending has been studied by mathematics over time
Mini-Workshop: Mathematics of Magnetoelastic Materials
No full textThe unifying theme of the workshop was the mathematical modeling, analysis, and numerical simulation of materials which involve magnetic and elastic interactions. During the workshop we identified several open problems from the calculus of variations, partial differential equations and modeling which appear to be essential in the understanding of the behavior of magnetoelastic materials
Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics
No full textRecently conjectures by Schmidt and by Davenport were solved in papers by Dzmitry Badziahin, Andrew Pollington and Sanju Velani, and by Victor Beresnevich. The methods which they used are the source for a growing number of works in Diophantine approximation, fractal geometry and flows on homogeneous spaces, and their full power is still far from being well understood. The goal of this workshop was to introduce those methods to a broader audience, and to allow for an opportunity to further their development
Toric Geometry
No full textToric geometry is a subfield of algebraic geometry with deep intersections with combinatorics. This workshop brought together researchers working in toric geometry, applying toric geometry elsewhere in algebraic geometry, and applying toric geometry elsewhere inside and outside mathematics
Singularities
No full textSingularity theory is a central part of contemporary mathematics. It is concerned with the local and global structure of maps and spaces that occur in algebraic, analytic or differential geometric context. For its study it uses methods from algebra, topology, algebraic geometry and complex analysis
Model Theory: groups, geometry, and combinatorics
No full textThis conference was about recent interactions of model theory with combinatorics, geometric group theory and the theory of valued fields, and the underlying pure model-theoretic developments. Its aim was to report on recent results in the area, and to foster communication between the different communities