Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Rough Paths, Regularity Structures and Related Topics
No full textThe purpose of the Oberwolfach workshop “Rough Paths and Regularity Structures” was to bring together these researchers, both young and senior, with the aim to consolidate progress in rough path theory and stochastic partial differential equations
Generalized Entropy Method for the Renewal Equation with Measure Data
No full textResearch in Pairs 2015We study the long-time asymptotics for the so-called McKendrick-Von Foerster or renewal equation, a simple model frequently considered in structured population dynamics. In contrast to previous works, we can admit a bounded measure as initial data. To this end, we apply techniques from the calculus of variations that have not been employed previously in this context. We demonstrate how the generalized relative entropy method can be refined in the Radon measure framework
The Initial and Terminal Cluster Sets of an Analytic Curve
No full textResearch in Pairs 2016For an analytic curve , the set of values approaches by , as and as can be any two continuua of
C*-Algebras
No full textThe field of operator algebras is a flourishing area of mathematics with strong ties to many other areas including functional/harmonic analysis, topology, (non-commutative) geometry, group theory and dynamical systems. The -Algebra workshop at Oberwolfach brings together leading experts and young researchers in all subjects where -algebras play a major role. The main goal of this meeting is to foster contacts and collaborations between researchers from different directions, as well as to highlight the main developments in the field
On the containment problem
No full textMathematicians routinely speak two languages: the language of geometry and the language of algebra. When translating between these languages, curves and lines become sets of polynomials called “ideals”. Often there are several possible translations. Then the mystery is how these possible translations relate to each other. We present how geometry itself gives insights into this question
Towards a Mathematical Theory of Turbulence in Fluids
No full textFluid mechanics is the theory of how liquids and gases move around. For the most part, the basic physics are well understood and the mathematical models look relatively simple. Despite this, fluids display a dazzling mystery to their motion. The random-looking, chaotic behavior of fluids is known as turbulence, and it lies far beyond our mathematical understanding, despite a century of intense research
Mathematical and Algorithmic Aspects of Data Assimilation in the Geosciences
No full textThe field of “Data Assimilation” has been driven by applications from the geosciences where complex mathematical models are interfaced with observational data in order to improve model forecasts. Mathematically, data assimilation is closely related to filtering and smoothing on the one hand and inverse problems and statistical inference on the other. Key challenges of data assimilation arise from the high-dimensionality of the underlying models, combined with systematic spatio-temporal model errors, pure model uncertainty quantification and relatively sparse observation networks. Advances in the field of data assimilation will require combination of a broad range of mathematical techniques from differential equations, statistics, machine learning, probability, scientific computing and mathematical modeling, together with insights from practitioners in the field. The workshop brought together a collection of scientists representing this broad spectrum of research strands
Wie steuert man einen Kran?
No full textDie Steuerung einer Last an einem Kran ist ein technisch und mathematisch schwieriges Problem, da die Bewegung der Last nur indirekt beeinflusst werden kann. Anhand eines Masse-Feder-Systems illustrieren wir diese Schwierigkeiten und zeigen wie man mit einem zum konventionellen Lösungsweg alternativen Optimierungsansatz die auftretenden Komplikationen teilweise umgehen kann
The Renormalization Group
No full textThe renormalization group was originally introduced as a multiscale approach to quantum field theory and the theory of critical phenomena, explaining in particular the universality observed e.g. in critical exponents. Since then it has become a hugely important tool in statistical mechanics, condensed matter and high energy physics. More recently, renormalization has also played a decisive role in mathematics as a method of proof, applicable in quantum field theory, differential equations, probability, and other fields. The workshop has focused on new developments along the lines of these two traditions. Besides discussing methodical progress and current applications, we have explored new challenges and problems that may in the future be tackled with the help of the renormalization group
Spherical Arc-Length as a Global Conformal Parameter for Analytic Curves in the Riemann Sphere
No full textResearch in Pairs 2016We prove that for every analytic curve in the complex plane , Euclidean and spherical arc-lengths are global conformal parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic arc-length is also a global parameter. We generalize some of these results to the case of analytic curves in and and we discuss the situation of curves in the Riemann sphere $\mathbb{C} \cup \{\infty\}.