http://publications.mfo.de/handle/mfo/2810 Oberwolfach Reports Volume 6 (2009) Thu, 09 Apr 2026 20:37:14 GMT 2026-04-09T20:37:14Z http://publications.mfo.de/handle/mfo/3158 Material Theories This biennial workshop brings together mathematicians, mechanicians and theoretical physicists interested in developing new mathematical models of complex materials, medias and systems. The workshop covers a wide range of topics from nonequilibrium statistical mechanics and dynamical systems to calculus of variations and nonlinear functional analysis. A particular focus of this meeting was on continuum description of biological systems, pattern formation, granular media, plasticity and turbulence. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3158 2009-01-01T00:00:00Z This biennial workshop brings together mathematicians, mechanicians and theoretical physicists interested in developing new mathematical models of complex materials, medias and systems. The workshop covers a wide range of topics from nonequilibrium statistical mechanics and dynamical systems to calculus of variations and nonlinear functional analysis. A particular focus of this meeting was on continuum description of biological systems, pattern formation, granular media, plasticity and turbulence. http://publications.mfo.de/handle/mfo/3157 Mini-Workshop: Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence The mini-workshop was devoted to the spectral analysis of random Schrödinger-type operators. While this topic has been intensively studo ied by physicists and mathematicians for several decades, more recently there has been particular attention devoted to models where the random parameters enter the model in a non-monotone or non-linear way. Most of the established methods applied for random operators, in fact, hinge on the presence of monotonicity w. r. t. randomness. Thus the treatment of non-monotone models forces a deeper analysis of the structure of random Hamiltonians and, in particular, the interplay of the kinetic and the potential energy parts. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3157 2009-01-01T00:00:00Z The mini-workshop was devoted to the spectral analysis of random Schrödinger-type operators. While this topic has been intensively studo ied by physicists and mathematicians for several decades, more recently there has been particular attention devoted to models where the random parameters enter the model in a non-monotone or non-linear way. Most of the established methods applied for random operators, in fact, hinge on the presence of monotonicity w. r. t. randomness. Thus the treatment of non-monotone models forces a deeper analysis of the structure of random Hamiltonians and, in particular, the interplay of the kinetic and the potential energy parts. http://publications.mfo.de/handle/mfo/3156 Mini-Workshop: The Escaping Set in Transcendental Dynamics The escaping set of a transcendental entire or meromorphic function consists of all points which tend to infinity under iteration. Its importance in transcendental dynamics has increased significantly in recent years. The workshop focussed on a study of this set. The topics considered include the geometry of the escaping set, its Hausdorff dimension, its relation to the Julia set, and various subsets of the escaping set defined in terms of escape rates. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3156 2009-01-01T00:00:00Z The escaping set of a transcendental entire or meromorphic function consists of all points which tend to infinity under iteration. Its importance in transcendental dynamics has increased significantly in recent years. The workshop focussed on a study of this set. The topics considered include the geometry of the escaping set, its Hausdorff dimension, its relation to the Julia set, and various subsets of the escaping set defined in terms of escape rates. http://publications.mfo.de/handle/mfo/3155 Mini-Workshop: Geometry of Quantum Entanglement The workshop aimed at developing interactions between researchers from quantum information theory and from asymptotic geometric analysis. A central notion discussed was the phenomenon of quantum entanglement, which naturally leads to geometric considerations in high-dimensional vector spaces. In these spaces, phenomena such as concentration of measure become prominent and may invalidate our low-dimensional intuition. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3155 2009-01-01T00:00:00Z The workshop aimed at developing interactions between researchers from quantum information theory and from asymptotic geometric analysis. A central notion discussed was the phenomenon of quantum entanglement, which naturally leads to geometric considerations in high-dimensional vector spaces. In these spaces, phenomena such as concentration of measure become prominent and may invalidate our low-dimensional intuition. http://publications.mfo.de/handle/mfo/3154 Convex Geometry and its Applications The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry, both the discrete and convex branches of it, has experienced a striking series of developments in the past 10 years. Several examples were presented at this meeting, for example the work of Rudelson et al. on conjunction matrices and their relation to confidential data analysis, that of Litvak et al. on remote sensing and a series of results by Nazarov and Ryabogin et al. on Mahler’s conjecture for the volume product of domains and their polars. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3154 2009-01-01T00:00:00Z The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry, both the discrete and convex branches of it, has experienced a striking series of developments in the past 10 years. Several examples were presented at this meeting, for example the work of Rudelson et al. on conjunction matrices and their relation to confidential data analysis, that of Litvak et al. on remote sensing and a series of results by Nazarov and Ryabogin et al. on Mahler’s conjecture for the volume product of domains and their polars. http://publications.mfo.de/handle/mfo/3153 Complexity Theory Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developements are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, quantum mechanics, representation theory, and the theory of error-correcting codes. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3153 2009-01-01T00:00:00Z Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developements are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, quantum mechanics, representation theory, and the theory of error-correcting codes. http://publications.mfo.de/handle/mfo/3152 Mini-Workshop: Spectrum of Transfer Operators: Recent Developments and Applications Transfer operators and their spectral theory provide a unifying framework for studying stochastic properties of chaotic deterministic dynamical systems. The goal of this workshop was to widen the class of systems that can be analysed in this way and to discuss and present new applications. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3152 2009-01-01T00:00:00Z Transfer operators and their spectral theory provide a unifying framework for studying stochastic properties of chaotic deterministic dynamical systems. The goal of this workshop was to widen the class of systems that can be analysed in this way and to discuss and present new applications. http://publications.mfo.de/handle/mfo/3151 Mini-Workshop: Feinstrukturtheorie und Innere Modelle This workshop presented recent advances in fine structure and inner model theory. There were extended tutorials on hod mice and the Mouse Set Conjecture, suitable extender sequences and their fine structure, and the construction of true K below a Woodin cardinal in ZFC. The remaining talks involved precipitous ideals, stationary set reflection, failure of SCH in ZF, nonthreadable square sequences, reverse mathematics, forcing axioms, covering properties of canonical inner models, and “set theoretic geology.” Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3151 2009-01-01T00:00:00Z This workshop presented recent advances in fine structure and inner model theory. There were extended tutorials on hod mice and the Mouse Set Conjecture, suitable extender sequences and their fine structure, and the construction of true K below a Woodin cardinal in ZFC. The remaining talks involved precipitous ideals, stationary set reflection, failure of SCH in ZF, nonthreadable square sequences, reverse mathematics, forcing axioms, covering properties of canonical inner models, and “set theoretic geology.” http://publications.mfo.de/handle/mfo/3150 Mini-Workshop: Formal Methods in Commutative Algebra: A View Toward Constructive Homological Algebra The purpose of the mini-workshop is to bring into the same place different mathematical communities that study constructive homological algebra and are motivated by different applications (e.g., constructive algebra, symbolic computation, proof theory, algebraic topology, mathematical systems theory, D-modules, dynamical systems theory) so that they can share their results, techniques, softwares and experiences. Through the development of a unified terminology, common mathematical problems, which naturally appear when making homological algebra constructive, were discussed. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3150 2009-01-01T00:00:00Z The purpose of the mini-workshop is to bring into the same place different mathematical communities that study constructive homological algebra and are motivated by different applications (e.g., constructive algebra, symbolic computation, proof theory, algebraic topology, mathematical systems theory, D-modules, dynamical systems theory) so that they can share their results, techniques, softwares and experiences. Through the development of a unified terminology, common mathematical problems, which naturally appear when making homological algebra constructive, were discussed. http://publications.mfo.de/handle/mfo/3149 Design and Analysis of Infectious Disease Studies This workshop gathered 45 participants from 16 countries and had a correspondingly multifaceted program covering various infectious diseases, public health applications, and methodological innovations. The discussions and presentations focused on the importance of mathematical models and statistical analyses in understanding the complex transmission systems of infectious diseases and in planning effective intervention strategies. Many different statistical and mathematical approaches were covered. The general unifying theme is that the analyses and models take into account the underlying transmission of the infectious agent among the hosts and/ or vector populations. Thu, 01 Jan 2009 00:00:00 GMT http://publications.mfo.de/handle/mfo/3149 2009-01-01T00:00:00Z This workshop gathered 45 participants from 16 countries and had a correspondingly multifaceted program covering various infectious diseases, public health applications, and methodological innovations. The discussions and presentations focused on the importance of mathematical models and statistical analyses in understanding the complex transmission systems of infectious diseases and in planning effective intervention strategies. Many different statistical and mathematical approaches were covered. The general unifying theme is that the analyses and models take into account the underlying transmission of the infectious agent among the hosts and/ or vector populations.