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- ItemReactive Flow and Transport Through Complex Systems(Zürich : EMS Publ. House, 2005) Mikelic, Andro; Schwab, ChristophThe meeting focused on mathematical aspects of reactive flow, diffusion and transport through complex systems. The research interest of the participants varied from physical modeling using PDEs, mathematical modeling using upscaling and homogenization, numerical analysis of PDEs describing reactive transport, PDEs from fluid mechanics, computational methods for random media and computational multiscale methods.
- ItemActions and Invariants of Residually Finite Groups: Asymptotic Methods(Zürich : EMS Publ. House, 2010) Gaboriau, Damien; Grunewald, FritzThe workshop brought together experts in finite group theory, L2-cohomology, measured group theory, the theory of lattices in Lie groups, probability and topology. The common object of interest was residually finite groups, that each field investigates from a different angle.
- ItemAlgebraic K-Theory(Zürich : EMS Publ. House, 2006) Huber-Klawitter, Annette; Jannsen, Uwe; Levine, MarcThis is the report on the Oberwolfach workshop Algebraic KTheory, held in July 2006. The talks covered mainly topics from Algebraic Geometry and Number Theory in connection with K-Theory. Special emphasis was placed on motivic cohomology and motivic homotopy of general schemes.
- ItemMini-Workshop: Shearlets(Zürich : EMS Publ. House, 2010) Labate, DemetrioOver the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing an efficient means for encoding isotropic phenomena. Directional multiscale systems, particularly shearlets, are now having the same dramatic impact on the encoding of multivariate signals. Since its introduction about five years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior way of achieving a truly unified treatment in both the continuum and digital setting. By now, shearlet analysis has reached maturity as a research field, with deep mathematical results, efficient numerical methods, and a variety of high-impact applications. The main goal of the Mini-Workshop Shearlets was to gather the world’s experts in this field in order to foster closer interaction, attack challenging open problems, and identify future research directions.
- ItemWavelet and Multiscale Methods(Zürich : EMS Publ. House, 2007) Dahmen, Wolfgang; DeVore, Ronald A.; Kunoth, AngelaVarious scientific models demand finer and finer resolutions of relevant features. Paradoxically, increasing computational power serves to even heighten this demand. Namely, the wealth of available data itself becomes a major obstruction. Extracting essential information from complex structures and developing rigorous models to quantify the quality of information leads to tasks that are not tractable by standard numerical techniques. The last decade has seen the emergence of several new computational methodologies to address this situation. Their common features are the nonlinearity of the solution methods as well as the ability of separating solution characteristics living on different length scales. Perhaps the most prominent examples lie in multigrid methods and adaptive grid solvers for partial differential equations. These have substantially advanced the frontiers of computability for certain problem classes in numerical analysis. Other highly visible examples are: regression techniques in nonparametric statistical estimation, the design of universal estimators in the context of mathematical learning theory and machine learning; the investigation of greedy algorithms in complexity theory, compression techniques and encoding in signal and image processing; the solution of global operator equations through the compression of fully populated matrices arising from boundary integral equations with the aid of multipole expansions and hierarchical matrices; attacking problems in high spatial dimensions by sparse grid or hyperbolic wavelet concepts. This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computation and to promote the exchange of ideas emerging in various disciplines.
- ItemAlgebraic K-Theory and Motivic Cohomology(Zürich : EMS Publ. House, 2009) Huber-Klawitter, Annette; Jannsen, Uwe; Levine, MarcAlgebraic K-theory and the related motivic cohomology are a systematic way of producing invariants for algebraic or geometric structures. Its definition and methods are taken from algebraic topology, but it has also proved particularly fruitful for problems of algebraic geometry, number theory or quadratic forms. 19 one-hour talks presented a wide range of results on K-theory itself and applications. We had a lively evening session trading questions and discussing open problems.
- ItemAlgebraic Groups(Zürich : EMS Publ. House, 2007) Jantzen, Jens Carsten; Rouquier, RaphaelThe workshop dealt with a broad range of topics from the structure theory and the representation theory of algebraic groups (in the widest sense). There was emphasis on the following areas: structure and classification of wonderful varieties, finite reductive groups and character sheaves, quantum cohomology of homogeneous varieties, representation categories and their connections to orbits and flag varieties.
- ItemArbeitsgemeinschaft: Percolation(Zürich : EMS Publ. House, 2007) van den Berg, Jacob; Camia, FedericoAbstract. Percolation as a mathematical theory is more than fifty years old. During its life, it has attracted the attention of both physicists and mathematicians. This is due in large part to the fact that it represents one of the simplest examples of a statistical mechanical model undergoing a phase transition, and that several interesting results can be obtained rigorously. In recent years the interest in percolation has spread even further, following the introduction by Oded Schramm of the Schramm-Loewner Evolution (SLE) and a theorem by Stanislav Smirnov showing the conformal invariance of the continuum scaling limit of two-dimensional critical percolation. These results establish a new, powerful and mathematically rigorous, link between lattice-based statistical mechanical models and conformally invariant models in the plane, studied by physicists under the name of Conformal Field Theory (CFT). The Arbeitsgemeinschaft on percolation has attracted more than thirty participants, most of them young researchers, from several countries in Europe, North America, and Brazil. The main focus has been on recent developments, but several classical results have also been presented.
- ItemStatistical Issues in Prediction: what can be learned for individualized predictive medicine?(Zürich : EMS Publ. House, 2010) Henderson, Robin; Mansmann, UlrichError is unavoidable in prediction. And it is quite common, often sizable, and usually consequential. In a clinical context, especially when dealing with a terminal illness, error in prediction of residual life means that patients and families are misinformed about their illness, that they may take foolish actions as a result, and that they may be given inappropriate or needlesly painful treatments or denied appropriate ones. In meteorology, error in prediction of storm paths or extreme events can have devastating consequences. In finance and economics, major policy decisions are taken on the basis of predictions and forecasts. Rational approaches to reduce and assess error in prediction are presented. Ideas are introduced how to relate these statistical strategies with clinical and medical concepts in particular and how to integrate ideas from apparently different areas.
- ItemControl Theory: On the Way to New Application Fields(Zürich : EMS Publ. House, 2009) Helmke, Uwe; Sontag, EduardoControl theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently, deep interactions are emerging with new application areas, such as systems biology, quantum control and information technology. In order to address the new challenges posed by the new application disciplines, a special focus of this workshop has been on the interaction between control theory and mathematical systems biology. To complement these more biology oriented focus, a series of lectures in this workshop was devoted to the control of networks of systems, fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control.