Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Variational Methods for Evolution
No full textMany evolutionary systems, as for example gradient flows or Hamiltonian systems, can be formulated in terms of variational principles or can be approximated using time-incremental minimization. Hence they can be studied using the mathematical techniques of the field of calculus of variations. This viewpoint has led to many discoveries and rapid expansion of the field over the last two decades. Relevant applications arise in mechanics of fluids and solids, in reaction-diffusion systems, in biology, in many-particle models, as well as in emerging uses in data science.
This workshop brought together a broad spectrum of researchers from calculus of variations, partial differential equations, metric geometry, and stochastics, as well as applied and computational scientists to discuss and exchange ideas. It focused on variational tools such as minimizing movement schemes, Gamma convergence, optimal transport, gradient flows, and large-deviation principles for time-continuous Markov processes
Statistical Recovery of Discrete, Geometric and Invariant Structures
No full textThe main objective of the workshop was to bring together researchers in mathematical statistics and related areas in order to discuss recent advances and problems associated with statistical recovery of geometric and invariant structures. Topics include adaptive estimation, confidence sets and testing techniques, as well as statistical algorithms for geometrical structure recovery and data analysis
Freeness of Multi-Reflection Arrangements via Primitive Vector Fields
No full textMSC: 20F55; 52C35; 14N20; 32S25Research in Pairs 2017In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to multi-arrangements stemming from well-generated unitary reflection groups, where the multiplicity of a hyperplane depends on the order of its stabilize. Here the exponents depend on the exponents of the dual reflection representation. When then extend our results further to all imprimitive irreducible unitary reflection groups. In this case the exponents turn out to depend on the exponents of a certain Galois twist of the dual reflection representation that comes from a Beynon-Lusztig type semi-palindromicity of fake degrees
Reaction Networks and Population Dynamics
No full textReaction systems and population dynamics constitute two highly developed areas of research that build on well-defined model classes, both in terms of dynamical systems and stochastic processes. Despite a significant core of common structures, the two fields have largely led separate lives. The workshop brought the communities together and emphasised concepts, methods and results that have, so far, appeared in one area but are potentially useful in the other as well
Mini-Workshop: Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions
No full textThis Mini-Workshop is devoted to regularity and numerical analysis of stochastic ordinary and partial differential equations (SDEs for both). The standard assumption in the literature on SDEs is global Lipschitz continuity of the coefficient functions. However, many SDEs arising from applications fail to have globally Lipschitz continuous coefficients. Recent years have seen a prosper growth of the literature on regularity and numerical approximations for SDEs with non-globally Lipschitz coefficients. Some surprising results have been obtained – e.g., the Euler–Maruyama method diverges for a large class of SDEs with super-linearly growing coefficients, and the limiting equation of a spatial discretization of the stochastic Burgers equation depends on whether the discretization is symmetric or not. Several positive results have been obtained. However the regularity of numerous important SDEs and the closely related question of convergence and convergence rates of numerical approximations remain open. The aim of this workshop is to bring together the main contributers in this direction and to foster significant progress
Geophysical Fluid Dynamics
No full textThe workshop “Geophysical Fluid Dynamics” addressed recent advances in analytical, stochastic, modeling and computational studies of geophysical fluid models. Of central interest were the reduced geophysical models, that are derived by means of asymptotic and scaling techniques, and their investigations by methods from the above disciplines. In particular, contributions concerning the viscous and inviscid geostrophic models, the primitive equations of oceanic and atmospheric dynamics, tropical atmospheric models and their coupling to nonlinear dynamics of phase changes moisture, thermodynamical effects, stratifying effects, as well as boundary layers were presented and discussed
L2
No full textMSC 2010: 41A17
Key words and phrases: Markov type inequalities, Gegenbauer polynomials, matrix normsResearch in Pairs 2016Let , where , be the Gegenbauer weight function, let
be the associated -norm, and denote by the space
of algebraic polynomials of degree .
We study the best constant in the Markov inequality in this
norm namely the constant We
derive explicit lower and upper bounds for the Markov constant ,
which are valid for all and
Komplexe Analysis
No full textComplex Analysis is a very active branch of mathematics. The aim of this workshop was to discuss recent developments in several complex variables and complex geometry. Topics included singular Kähler–Einstein metrics, positivity of higher direct images, cycle spaces and extension theorems
Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950
No full textSince 1950, mathematicians have become increasingly familiar with the digital computer in their professional practice. Previously, however, many other instruments, now mostly forgotten, were commonly used to compute numerical solutions, generate geometrical objects, investigate mathematical problems, derive new results, and apply mathematics in a variety of scientific contexts. The problem of characterizing the mathematical objects that can be constructed with a given set of instruments frequently prompted deep theoretical investigations, from the Euclidean geometry of constructions with straightedge and compass, to Shannon’s theorem which, in 1941, stated that the functions constructible with a differential analyzer are exactly the solutions of algebraic differential equations. Beyond these mathematical considerations, instruments should also be viewed as social objects of a given time period and cultural tradition that can amalgamate the perspectives of the inventor, the maker, the user, and the collector; in this sense, mathematical instruments are an important part of the mathematical cultural heritage and are thus widely used in many science museums to demonstrate the cultural value of mathematics to the public. This workshop brought together mathematicians, historians, philosophers, collection curators, and scholars of education to address the various approaches to the history of mathematical instruments and compare the definition and role of these instruments over time, with the following fundamental questions in mind – What is mathematical in a mathematical instrument? What kind of mathematics is involved? What does it mean to embody mathematics in a material artefact, and how do non-mathematicians engage with this kind of embodied mathematics
Locally Compact Abelian p-Groups Revisited
No full textResearch in Pairs 2017Even though the structure of locally compact abelian groups is generally considered to be rather thoroughly known through a wealth of publications, one keeps encountering corners that are not elucidated in up-to-date literature. In a study of a particular class of metabelian locally compact groups (see [HHR17]) we encountered some issues about noncompact locally compact abelian groups which do not appear to be discussed in the literature even though some of them were anticipated in Braconnier's article on his local product [Bra48]. Here we treat some of them, notably some aspects of totally disconnected torsion-free locally compact abelian groups which one might consider unexpected if not pathological. However, firstly we deal with some points concerning
noncompact locally compact abelian torsion groups. For compact abelian groups we often refer to the monograph [HM13]. It will be convenient to use additive notation for abelian groups