Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Factorization Algebras and Functorial Field Theories
No full textFactorization algebras are a new mathematical approach to quantum field theory. They are related to functorial field theories, another approach to quantum field theory. Factorization algebras also figure in current research in manifold topology, homotopy theory and algebraic geometry. The workshop brought together researchers from many different fields to understand and deepen these connections
Heat Kernels, Stochastic Processes and Functional Inequalities
No full textThe general topic of the 2016 workshop Heat kernels, stochastic processes and functional inequalities was the study of linear and non-linear diffusions in geometric environments including smooth manifolds, fractals and graphs, metric spaces and in random environments. The workshop brought together leading researchers from analysis, geometry and probability, and provided an excellent opportunity for interactions between scientists from these areas at different stages of their career. The unifying themes were heat kernel analysis, mass transportation problems and functional inequalities while the program straddled across a great variety of subjects and across the divide that exists between discrete and continuous mathematics. Other unifying concepts such as the notions of metric measure space, Otto Calculus and Lott-Sturm-Villani synthetic Ricci curvature bounds played an important part in the discussions. Novel directions including the study of Liouville quantum gravity were included. The workshop provided participants with an opportunity to discuss how these ideas and techniques can be used to approach problems regarding optimal transport, Riemannian and sub-Riemannian geometry, and analysis and stochastic processes in random media
Theory and Numerics of Inverse Scattering Problems
No full textThis workshop addressed specific inverse problems for the time-harmonic Maxwell’s equations, resp. special cases of these, such as the Helmholtz equation or quasistatic approximations like in impedance tomography. The inverse problems considered include the reconstruction of obstacles and/or their material properties in a known background, given various kinds of data, such as near or far field measurements in the scattering context and boundary measurements in the quasistatic case
High performance computing on smartphones
No full textNowadays there is a strong demand to simulate even real-world engineering problems on small computing devices with very limited capacity, such as a smartphone. We explain, using a concrete example, how we can obtain a reduction in complexity – to enable such computations – using mathematical methods
Adaptive Algorithms
No full textOverwhelming empirical evidence in computational science and engineering proved that self-adaptive mesh-generation is a must-do in real-life problem computational partial differential equations. The mathematical understanding of corresponding algorithms concerns the overlap of two traditional mathematical disciplines, numerical analysis and approximation theory, with computational sciences. The half workshop was devoted to the mathematics of optimal convergence rates and instance optimality of the Dörfler marking or the maximum strategy in various versions of space discretisations and time-evolution problems with all kind of applications in the efficient numerical treatment of partial differential equations
Rational Approximation on Products of Planar Domains
No full textResearch in Pairs 2015We consider , the Banach space of functions from to that are continuous with respect to the product topology and separately holomorphic, where is an arbitrary set and are planar domains of some type. We show that finite sums of finite products of rational functions of one variable with prescribed poles off are uniformly dense in . This generalizes previous results where is the open unit disc in or is connected
Footballs and donuts in four dimensions
No full textIn this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world and then discuss the ways one may generalize these ideas into higher dimensions
Killing Tensors on Tori
No full textResearch in Pairs 2016We show that Killing tensors on conformally at n-dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral of the geodesic flow polynomial in the momenta on the sphere bundle of such a torus is linear in the momenta
Lattices and Applications in Number Theory
No full textThis is a report on the workshop on Lattices and Applications in Number Theory held in Oberwolfach, from January 17 to January 23, 2016. The workshop brought together people working in various areas related to the field: classical geometry of numbers, packings, Diophantine approximation, Arakelov geometry, cohomology of arithmetic groups, algebraic modular forms and Hecke operators, algebraic topology. The meeting consisted of a few long talks which included an introductory part to each of the topics in the previous list, and a series of shorter talks mainly devoted to recent developments. The present report contains extended abstracts of all presentations
Mechanics of Materials: Mechanics of Interfaces and Evolving Microstructure
No full textEmphasis in modern day efforts in mechanics of materials is increasingly directed towards integration with computational materials science, which itself rests on solid physical and mathematical foundations in thermodynamics and kinetics of processes. Practical applications demand attention to length and time scales which are sufficiently large to preclude direct application of quantum mechanics approaches; accordingly, there are numerous pathways to mathematical modelling of the complexity of material structure during processing and in service. The conventional mathematical machinery of energy minimization provides guidance but has limited direct applicability to material systems evolving away from equilibrium. Material response depends on driving forces, whether arising from mechanical, electromagnetic, or thermal fields. When microstructures evolve, as during plastic deformation, progressive damage and fracture, corrosion, stress-assisted diffusion, migration or chemical/thermal aging, the associated classical mathematical frameworks are often ad hoc and heuristic. Advancing new and improved methods is a major focus of 21st century mechanics of materials of interfaces and evolving microstructure