http://publications.mfo.de/handle/mfo/2806 Oberwolfach Reports Volume 2 (2005) Sat, 11 Apr 2026 10:56:54 GMT 2026-04-11T10:56:54Z http://publications.mfo.de/handle/mfo/2930 Mathematics in the Physical Sciences, 1650-2000 The workshop “Mathematics in the Physical Sciences, 1650-2000” was organised by Niccolò Guicciardini (Siena), Tinne Hoff Kjeldsen (Roskilde), and David Rowe (Mainz). By focusing on the interplay between mathematics and the physical sciences the aim was to gain an insight into developments that had a crucial impact on modern mathematics. Three particular topics emerged as central themes: 1) The period 1650-1800 raises many issues related to the role of mathematics in natural philosophy during the Scientific Revolution and the Enlightenment. Discussing these issues can enhance our historical understanding of a period in which mechanics, astronomy, navigation, cartography, hydraulics, etc., constituted an important stimulus for advances in mathematics. 2) The period 1800-1920 centred on the problem of probing the geometry of space both mathematically and empirically after the advent of non-Euclidean geometry. 3) The twentieth century was focused on mathematical modelling and the question of a change in the conception of mathematical models in various disciplines after 1900. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2930 2005-01-01T00:00:00Z The workshop “Mathematics in the Physical Sciences, 1650-2000” was organised by Niccolò Guicciardini (Siena), Tinne Hoff Kjeldsen (Roskilde), and David Rowe (Mainz). By focusing on the interplay between mathematics and the physical sciences the aim was to gain an insight into developments that had a crucial impact on modern mathematics. Three particular topics emerged as central themes: 1) The period 1650-1800 raises many issues related to the role of mathematics in natural philosophy during the Scientific Revolution and the Enlightenment. Discussing these issues can enhance our historical understanding of a period in which mechanics, astronomy, navigation, cartography, hydraulics, etc., constituted an important stimulus for advances in mathematics. 2) The period 1800-1920 centred on the problem of probing the geometry of space both mathematically and empirically after the advent of non-Euclidean geometry. 3) The twentieth century was focused on mathematical modelling and the question of a change in the conception of mathematical models in various disciplines after 1900. http://publications.mfo.de/handle/mfo/2929 Set Theory This meeting covered all important aspects of modern Set Theory, including large cardinal theory, combinatorial set theory, descriptive set theory, connections with algebra and analysis, forcing axioms and inner model theory. The presence of an unusually large number (19) of young researchers made the meeting especially dynamic. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2929 2005-01-01T00:00:00Z This meeting covered all important aspects of modern Set Theory, including large cardinal theory, combinatorial set theory, descriptive set theory, connections with algebra and analysis, forcing axioms and inner model theory. The presence of an unusually large number (19) of young researchers made the meeting especially dynamic. http://publications.mfo.de/handle/mfo/2928 Heat Kernels, Stochastic Processes and Functional Inequalities The conference brought together mathematicians belonging to several fields, essentially analysis, probability and geometry. One of the main unifying topics was certainly the study of heat kernels in various contexts: fractals, manifolds, domains of the Euclidean space, percolation clusters, infinite dimensional spaces, metric measure spaces. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2928 2005-01-01T00:00:00Z The conference brought together mathematicians belonging to several fields, essentially analysis, probability and geometry. One of the main unifying topics was certainly the study of heat kernels in various contexts: fractals, manifolds, domains of the Euclidean space, percolation clusters, infinite dimensional spaces, metric measure spaces. http://publications.mfo.de/handle/mfo/2927 Mini-Workshop: Heterotic Strings, Derived Categories, and Stacks This workshop brought together both mathematicians and physicists interested in mathematical aspects of heterotic strings and physical aspects of derived categories and stacks. These three topics in mathematics and physics are all involved in modern approaches to and extensions of mirror symmetry, and much of the technical machinery in understanding their physics and mathematics overlap, so by bringing together experts in these areas we hope to help spur further developments. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2927 2005-01-01T00:00:00Z This workshop brought together both mathematicians and physicists interested in mathematical aspects of heterotic strings and physical aspects of derived categories and stacks. These three topics in mathematics and physics are all involved in modern approaches to and extensions of mirror symmetry, and much of the technical machinery in understanding their physics and mathematics overlap, so by bringing together experts in these areas we hope to help spur further developments. http://publications.mfo.de/handle/mfo/2926 Mini-Workshop: Dynamics of Cocycles and One-Dimensional Spectral Theory Many spectral questions about one-dimensional Schrödinger operators with quasi-periodic potentials can be reduced to dynamical questions about certain quasi-periodic SL(2, R)-valued cocycles. This connection has recently been employed to prove a number of long-standing conjectures. The aim of this mini-workshop was to bring together people from both spectral theory and dynamical systems in order to further develop and exploit the dynamical approach to quasi-periodic Schrödinger operators. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2926 2005-01-01T00:00:00Z Many spectral questions about one-dimensional Schrödinger operators with quasi-periodic potentials can be reduced to dynamical questions about certain quasi-periodic SL(2, R)-valued cocycles. This connection has recently been employed to prove a number of long-standing conjectures. The aim of this mini-workshop was to bring together people from both spectral theory and dynamical systems in order to further develop and exploit the dynamical approach to quasi-periodic Schrödinger operators. http://publications.mfo.de/handle/mfo/2925 Mini-Workshop: Analysis and Computation of Microstructures in Finite Plasticity Plastic material behaviour is typically the result of the interaction of complex substructures on a microscopic scale. Common models of finite plasticity are based on macroscopic, phenomenological approaches and do not take into account any microstructural information. The miniworkshop focuses on the application of methods from the calculus of variations to models for microstructures in plasticity. In particular, the investigation of the relaxation of the underlying functional, corresponding to quasiconvexification of the energy density, allows us to gain interesting microscopic as well as macroscopic information. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2925 2005-01-01T00:00:00Z Plastic material behaviour is typically the result of the interaction of complex substructures on a microscopic scale. Common models of finite plasticity are based on macroscopic, phenomenological approaches and do not take into account any microstructural information. The miniworkshop focuses on the application of methods from the calculus of variations to models for microstructures in plasticity. In particular, the investigation of the relaxation of the underlying functional, corresponding to quasiconvexification of the energy density, allows us to gain interesting microscopic as well as macroscopic information. http://publications.mfo.de/handle/mfo/2924 Combinatorial Optimization This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. The lectures show the many connections to other branches in Mathematics, like Combinatorics, Graph Theory, Geometry and Integer Programming. Furthermore, there are important connections to Theoretical Computer Science, Operations Research and an ever-growing number of application areas. Differing research directions in Combinatorial Optimization, current hot topics as well as classical streams were present in the talks. As can be seen from the table of contents, we strived for a balanced mixture of basic theoretical advancements and some selected practical applications. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2924 2005-01-01T00:00:00Z This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. The lectures show the many connections to other branches in Mathematics, like Combinatorics, Graph Theory, Geometry and Integer Programming. Furthermore, there are important connections to Theoretical Computer Science, Operations Research and an ever-growing number of application areas. Differing research directions in Combinatorial Optimization, current hot topics as well as classical streams were present in the talks. As can be seen from the table of contents, we strived for a balanced mixture of basic theoretical advancements and some selected practical applications. http://publications.mfo.de/handle/mfo/2923 Reactive Flow and Transport Through Complex Systems The 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. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2923 2005-01-01T00:00:00Z The 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. http://publications.mfo.de/handle/mfo/2922 Noncommutative Geometry and Quantum Field Theory The workshop gathered experts from both mathemematics and physics working on the interrelation of Noncommutative Geometry and Quantum Field Theory, which has become one of the central topics in mathematical physics over the last decade. The talks mainly focused on the possible noncommuativity of spacetime, applications of the local index formula in quantum field theory and the significant recent progress concerning the construction of interacting quantum field theories over noncommutative spaces. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2922 2005-01-01T00:00:00Z The workshop gathered experts from both mathemematics and physics working on the interrelation of Noncommutative Geometry and Quantum Field Theory, which has become one of the central topics in mathematical physics over the last decade. The talks mainly focused on the possible noncommuativity of spacetime, applications of the local index formula in quantum field theory and the significant recent progress concerning the construction of interacting quantum field theories over noncommutative spaces. http://publications.mfo.de/handle/mfo/2921 Statistische und Probabilistische Methoden der Modellwahl Aim of this conference with more than 50 participants, was to bring together leading researchers from roughly three different scientific communities who work on the same issue, data based model selection. Their different methodological approaches can be roughly classified into (1) Frequentist model selection and testing (2) Statistical learning theory and machine learning (3) Bayesian model selection The key task in model selection is to select a proper mathematical model based on information generated by data and/or by prior knowledge. Proper might mean a model with minimal prediction error, a model which describes the main qualitative data features, such as bumps and modes, or a model of low computational complexity. Mathematical techniques and concepts encountered with this workshop are wide spread, ranging from concentration and oracle inequalities, asymptotic analysis and distribution theory to testing theory, information measures and nonconvex optimization. Sat, 01 Jan 2005 00:00:00 GMT http://publications.mfo.de/handle/mfo/2921 2005-01-01T00:00:00Z Aim of this conference with more than 50 participants, was to bring together leading researchers from roughly three different scientific communities who work on the same issue, data based model selection. Their different methodological approaches can be roughly classified into (1) Frequentist model selection and testing (2) Statistical learning theory and machine learning (3) Bayesian model selection The key task in model selection is to select a proper mathematical model based on information generated by data and/or by prior knowledge. Proper might mean a model with minimal prediction error, a model which describes the main qualitative data features, such as bumps and modes, or a model of low computational complexity. Mathematical techniques and concepts encountered with this workshop are wide spread, ranging from concentration and oracle inequalities, asymptotic analysis and distribution theory to testing theory, information measures and nonconvex optimization.