http://publications.mfo.de/handle/mfo/2814 Oberwolfach Reports Volume 10 (2013) Wed, 08 Apr 2026 11:37:46 GMT 2026-04-08T11:37:46Z http://publications.mfo.de/handle/mfo/3390 Material Theories The subject of this meeting was mathematical modeling of strongly interacting multi-particle systems that can be interpreted as advanced materials. The main emphasis was placed on contributions attempting to bridge the gap between discrete and continuum approaches, focusing on the multi-scale nature of physical phenomena and bringing new and nontrivial mathematics. The mathematical debates concentrated on nonlinear PDE, stochastic dynamical systems, optimal transportation, calculus of variations and large deviations theory. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3390 2013-01-01T00:00:00Z The subject of this meeting was mathematical modeling of strongly interacting multi-particle systems that can be interpreted as advanced materials. The main emphasis was placed on contributions attempting to bridge the gap between discrete and continuum approaches, focusing on the multi-scale nature of physical phenomena and bringing new and nontrivial mathematics. The mathematical debates concentrated on nonlinear PDE, stochastic dynamical systems, optimal transportation, calculus of variations and large deviations theory. http://publications.mfo.de/handle/mfo/3389 Cluster Algebras and Related Topics Cluster algebras are a class of commutative algebras intoduced by Fomin and Zelevinsky in 2000. Their original purpose was to obtain a combinatorial approach to Lusztig’s dual canonical bases of quantum groups and to total positivity. Since then numerous connections between other areas of mathematics have been discovered. The aim of this workshop was to further strengthen these connections and to develop interactions. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3389 2013-01-01T00:00:00Z Cluster algebras are a class of commutative algebras intoduced by Fomin and Zelevinsky in 2000. Their original purpose was to obtain a combinatorial approach to Lusztig’s dual canonical bases of quantum groups and to total positivity. Since then numerous connections between other areas of mathematics have been discovered. The aim of this workshop was to further strengthen these connections and to develop interactions. http://publications.mfo.de/handle/mfo/3388 Classical and Quantum Mechanical Models of Many-Particle Systems This meeting was focused on recent results on the mathematical analysis of many-particle systems, both classical and quantum-mechanical in scaling regimes such that the methods of kinetic theory can be expected to apply. Thus, the Boltzmann equation is in many ways the central equation investigated in much of the research presented and discussed at this meeting, but the range of topics naturally extended from this center to include other non-linear partial differential and integro-differential equations, especially macroscopic/fluid-dynamical limits of kinetic equations modeling the dynamics of many-particle systems. A significant subset of the talks focused on propagation of chaos, and the validation and derivation of kinetic equations from underlying stochastic particle models in which there has been much progress and activity. Models were discussed with applications not only in physics, but also engineering, and mathematical biology. While there were a number of new participants, especially younger researchers, an interesting aspect of the conference was the number of talks presenting progress that had its origins in the previous meeting in this series held in 2010. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3388 2013-01-01T00:00:00Z This meeting was focused on recent results on the mathematical analysis of many-particle systems, both classical and quantum-mechanical in scaling regimes such that the methods of kinetic theory can be expected to apply. Thus, the Boltzmann equation is in many ways the central equation investigated in much of the research presented and discussed at this meeting, but the range of topics naturally extended from this center to include other non-linear partial differential and integro-differential equations, especially macroscopic/fluid-dynamical limits of kinetic equations modeling the dynamics of many-particle systems. A significant subset of the talks focused on propagation of chaos, and the validation and derivation of kinetic equations from underlying stochastic particle models in which there has been much progress and activity. Models were discussed with applications not only in physics, but also engineering, and mathematical biology. While there were a number of new participants, especially younger researchers, an interesting aspect of the conference was the number of talks presenting progress that had its origins in the previous meeting in this series held in 2010. http://publications.mfo.de/handle/mfo/3387 Numerical Solution of PDE Eigenvalue Problems This workshop brought together researchers from many different areas of numerical analysis, scientific computing and application areas, ranging from quantum mechanics, acoustic field computation to material science, working on eigenvalue problems for partial differential equations. Major challenges and new research directions were identified and the interdisciplinary cooperation was strengthened through a very lively workshop with many discussions. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3387 2013-01-01T00:00:00Z This workshop brought together researchers from many different areas of numerical analysis, scientific computing and application areas, ranging from quantum mechanics, acoustic field computation to material science, working on eigenvalue problems for partial differential equations. Major challenges and new research directions were identified and the interdisciplinary cooperation was strengthened through a very lively workshop with many discussions. http://publications.mfo.de/handle/mfo/3386 Design and Analysis of Infectious Disease Studies The fourth workshop on this theme is devoted to the statistical problems of planning and analyzing studies in infectious disease epidemiology. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3386 2013-01-01T00:00:00Z The fourth workshop on this theme is devoted to the statistical problems of planning and analyzing studies in infectious disease epidemiology. http://publications.mfo.de/handle/mfo/3385 Mini-Workshop: Inelastic and Non-equilibrium Material Behavior: from Atomistic Structure to Macroscopic Constitutive Relations The workshop brought together 15 scientists, which included leaders in the fields of mathematics (partial differential equations, statistical mechanics and calculus of variations) and mechanics (continuum mechanics, computational mechanics, microstructure and material science) as well as mid- and early-career participants. We addressed the themes of modeling crystal plasticity, crystallization and fracture, and non-equilibrium thermodynamics. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3385 2013-01-01T00:00:00Z The workshop brought together 15 scientists, which included leaders in the fields of mathematics (partial differential equations, statistical mechanics and calculus of variations) and mechanics (continuum mechanics, computational mechanics, microstructure and material science) as well as mid- and early-career participants. We addressed the themes of modeling crystal plasticity, crystallization and fracture, and non-equilibrium thermodynamics. http://publications.mfo.de/handle/mfo/3384 Mini-Workshop: Quaternion Kähler Structures in Riemannian and Algebraic Geometry Metrics of special holonomy are of central interest in both Riemannian and complex algebraic geometry. We focus on an important classification problem of a particular type of special holonomy manifolds, namely compact quaternion-Kähler with positive scalar curvature (Salamon-LeBrun conjecture). In the language of algebraic geometry this corresponds to the classification of Fano contact manifolds. By bringing together leading experts in both fields this workshop pursued a two-fold goal: First, to revise old and to develop new strategies for proving the most central conjecture in the field of quaternionic Kähler geometry. Second, to introduce young researchers at PhD/PostDoc level to this interdisciplinary circle of ideas. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3384 2013-01-01T00:00:00Z Metrics of special holonomy are of central interest in both Riemannian and complex algebraic geometry. We focus on an important classification problem of a particular type of special holonomy manifolds, namely compact quaternion-Kähler with positive scalar curvature (Salamon-LeBrun conjecture). In the language of algebraic geometry this corresponds to the classification of Fano contact manifolds. By bringing together leading experts in both fields this workshop pursued a two-fold goal: First, to revise old and to develop new strategies for proving the most central conjecture in the field of quaternionic Kähler geometry. Second, to introduce young researchers at PhD/PostDoc level to this interdisciplinary circle of ideas. http://publications.mfo.de/handle/mfo/3383 Large Scale Stochastic Dynamics In focus are interacting stochastic systems with many components, ranging from stochastic partial differential equations to discrete systems as interacting particles on a lattice moving through random jumps. More specifically one wants to understand the large scale behavior, large in spatial extent but also over long time spans, as entailed by the characterization of stationary measures, effective macroscopic evolution laws, transport of conserved fields, homogenization, self-similar structure and scaling, critical dynamics, dynamical phase transitions, metastability, large deviations, to mention only a few key items. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3383 2013-01-01T00:00:00Z In focus are interacting stochastic systems with many components, ranging from stochastic partial differential equations to discrete systems as interacting particles on a lattice moving through random jumps. More specifically one wants to understand the large scale behavior, large in spatial extent but also over long time spans, as entailed by the characterization of stationary measures, effective macroscopic evolution laws, transport of conserved fields, homogenization, self-similar structure and scaling, critical dynamics, dynamical phase transitions, metastability, large deviations, to mention only a few key items. http://publications.mfo.de/handle/mfo/3382 Analytic Number Theory Analytic number theory has florished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subject. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3382 2013-01-01T00:00:00Z Analytic number theory has florished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subject. http://publications.mfo.de/handle/mfo/3381 Arbeitsgemeinschaft: Sofic Entropy The notion of soficity for a group is a weak type of finite approximation property that simultaneously generalizes both amenability and residual finiteness. In 2008 L. Bowen discovered how it can be used to significantly broaden the scope of the classical theory of dynamical entropy beyond the setting of amenable acting groups. This Arbeitsgemeinschaft aimed to provide a comprehensive picture of the subject of sofic entropy as it has developed over the last five years. Tue, 01 Jan 2013 00:00:00 GMT http://publications.mfo.de/handle/mfo/3381 2013-01-01T00:00:00Z The notion of soficity for a group is a weak type of finite approximation property that simultaneously generalizes both amenability and residual finiteness. In 2008 L. Bowen discovered how it can be used to significantly broaden the scope of the classical theory of dynamical entropy beyond the setting of amenable acting groups. This Arbeitsgemeinschaft aimed to provide a comprehensive picture of the subject of sofic entropy as it has developed over the last five years.