http://publications.mfo.de/handle/mfo/2808 Oberwolfach Reports Volume 4 (2007) Wed, 08 Apr 2026 14:03:05 GMT 2026-04-08T14:03:05Z http://publications.mfo.de/handle/mfo/3044 Material Theories The workshop reviewed classical and recent trends in the modeling of material behavior using a wide spectrum of mathematical tools (stochastic processes, calculus of variations, pde’s). Among the topic covered, the following figured prominently: biology and biophysics, mechanics of nanostuctures, crystal plasticity, self-organized criticality, non equilibrium statistical mechanics, quantum mechanics, wetting phenomena, electronic transport in semiconductors, dislocation mechanics, kinetic theory, bucking in structural mechanics. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3044 2007-01-01T00:00:00Z The workshop reviewed classical and recent trends in the modeling of material behavior using a wide spectrum of mathematical tools (stochastic processes, calculus of variations, pde’s). Among the topic covered, the following figured prominently: biology and biophysics, mechanics of nanostuctures, crystal plasticity, self-organized criticality, non equilibrium statistical mechanics, quantum mechanics, wetting phenomena, electronic transport in semiconductors, dislocation mechanics, kinetic theory, bucking in structural mechanics. http://publications.mfo.de/handle/mfo/3043 Tropical Geometry Tropical Geometry is a new and rapidly developing discipline that touches upon many branches of modern mathematics. It is characterized by the transition of algebro-geometric objects to piecewise-linear ones, thereby retaining much of the algebro-geometric data while unveiling novel sets of techniques for outstanding problems. The workshop provided an invaluable communication platform as the subject develops into a field of its own. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3043 2007-01-01T00:00:00Z Tropical Geometry is a new and rapidly developing discipline that touches upon many branches of modern mathematics. It is characterized by the transition of algebro-geometric objects to piecewise-linear ones, thereby retaining much of the algebro-geometric data while unveiling novel sets of techniques for outstanding problems. The workshop provided an invaluable communication platform as the subject develops into a field of its own. http://publications.mfo.de/handle/mfo/3042 Coding Theory Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete mathematics and combinatorics, complexity theory, and statistical physics. The workshop on coding theory covered many facets of the recent research advances. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3042 2007-01-01T00:00:00Z Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete mathematics and combinatorics, complexity theory, and statistical physics. The workshop on coding theory covered many facets of the recent research advances. http://publications.mfo.de/handle/mfo/3041 Mini-Workshop: Surface Modeling and Syzygies The problem of determining the implicit equation of the image of a rational map φ : P2 99K P3 is of theoretical interest in algebraic geometry, and of practical importance in geometric modeling. There are essentially three methods which can be applied to the problem: Gröbner bases, resultants, and syzygies. Elimination via Gröbner basis methods tends to be computationally intensive and, being a general tool, is not adapted to the geometry of specific problems. Thus, it is primarily the latter two techniques which are used in practice. This is an extremely active area of research where many different perspectives come into play. The mini-workshop brought together a diverse group of researchers with different areas of expertise. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3041 2007-01-01T00:00:00Z The problem of determining the implicit equation of the image of a rational map φ : P2 99K P3 is of theoretical interest in algebraic geometry, and of practical importance in geometric modeling. There are essentially three methods which can be applied to the problem: Gröbner bases, resultants, and syzygies. Elimination via Gröbner basis methods tends to be computationally intensive and, being a general tool, is not adapted to the geometry of specific problems. Thus, it is primarily the latter two techniques which are used in practice. This is an extremely active area of research where many different perspectives come into play. The mini-workshop brought together a diverse group of researchers with different areas of expertise. http://publications.mfo.de/handle/mfo/3040 Mini-Workshop: Arithmetik von Gruppenringen The theory of group rings has many connections to other mathematical areas, such as number theory, K-theory, topology, representation theory, homological algebra and of course the theory of finite and infinite groups, and ring theory. This mini workshop focussed on the arithmetics of integral group rings, particularly their multiplicative structure and unit groups. The central topics were the recent developments in connection with the first Zassenhaus conjecture, constructive descriptions of units and subgroups of units, cohomological and representation theoretical methods, a complete description of the units of integral group rings of some classes of finite groups, and interactions with semigroup rings and orders. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3040 2007-01-01T00:00:00Z The theory of group rings has many connections to other mathematical areas, such as number theory, K-theory, topology, representation theory, homological algebra and of course the theory of finite and infinite groups, and ring theory. This mini workshop focussed on the arithmetics of integral group rings, particularly their multiplicative structure and unit groups. The central topics were the recent developments in connection with the first Zassenhaus conjecture, constructive descriptions of units and subgroups of units, cohomological and representation theoretical methods, a complete description of the units of integral group rings of some classes of finite groups, and interactions with semigroup rings and orders. http://publications.mfo.de/handle/mfo/3039 Mini-Workshop: Theory and Numerics of Fluid-Solid Interaction This volume contains the abstracts of a series of talks given at a mini-workshop in Oberwolfach on the theory and numerics of continuum mechanical fluid-solid/structure interaction. The characteristics of these coupled multi-field problems are that the displacement of the solid/structure has a direct influence on the surrounding flow and vice versa. This interaction is generally nonlinear making the modeling complicated. The mathematical analysis concentrates on the well-posedness of the models in order to provide a rigorous explanation of fundamental experiments. Various competing numerical approaches are discussed based on different variational formulations and mainly using finite element methods. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3039 2007-01-01T00:00:00Z This volume contains the abstracts of a series of talks given at a mini-workshop in Oberwolfach on the theory and numerics of continuum mechanical fluid-solid/structure interaction. The characteristics of these coupled multi-field problems are that the displacement of the solid/structure has a direct influence on the surrounding flow and vice versa. This interaction is generally nonlinear making the modeling complicated. The mathematical analysis concentrates on the well-posedness of the models in order to provide a rigorous explanation of fundamental experiments. Various competing numerical approaches are discussed based on different variational formulations and mainly using finite element methods. http://publications.mfo.de/handle/mfo/3038 Professional Development of Mathematics Teachers - Research and Practice from an International Perspective The Oberwolfach Workshop on “Teachers Professional Development” gathered a wide spectrum of topics of international research and practice in the field of mathematics education. Well-known researchers from all over the world explored the theme from various angles and with different emphasis ranging from theoretical and conceptual perspectives to empirical interventions. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3038 2007-01-01T00:00:00Z The Oberwolfach Workshop on “Teachers Professional Development” gathered a wide spectrum of topics of international research and practice in the field of mathematics education. Well-known researchers from all over the world explored the theme from various angles and with different emphasis ranging from theoretical and conceptual perspectives to empirical interventions. http://publications.mfo.de/handle/mfo/3037 Modulformen The meeting brought together 24 mathematicas working on some of the many aspects of modular forms. The main focus was on holomorphic modular forms (mainly in many variables). This theory is very rich in explicit structures. Central themes were explicit liftings and their properties and the detailed study of modular forms for GSp(4), as well as relations to arithmetic and algebraic geometry. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3037 2007-01-01T00:00:00Z The meeting brought together 24 mathematicas working on some of the many aspects of modular forms. The main focus was on holomorphic modular forms (mainly in many variables). This theory is very rich in explicit structures. Central themes were explicit liftings and their properties and the detailed study of modular forms for GSp(4), as well as relations to arithmetic and algebraic geometry. http://publications.mfo.de/handle/mfo/3036 Reassessing the Paradigms of Statistical Model-Building Statistical model-building is the science of constructing models from data and from information about the data-generation process, with the aim of analysing those data and drawing inference from that analysis. Many statistical tasks are undertaken during this analysis; they include classification, forecasting, prediction and testing. Model-building has assumed substantial importance, as new technologies enable data on highly complex phenomena to be gathered in very large quantities. This creates a demand for more complex models, and requires the model-building process itself to be adaptive. The word “paradigm” refers to philosophies, frameworks and methodologies for developing and interpreting statistical models, in the context of data, and applying them for inference. In order to solve contemporary statistical problems it is often necessary to combine techniques from previously separate paradigms. The workshop addressed model-building paradigms that are at the frontiers of modern statistical research. It tried to create synergies, by delineating the connections and collisions among different paradigms. It also endeavoured to shape the future evolution of paradigms. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3036 2007-01-01T00:00:00Z Statistical model-building is the science of constructing models from data and from information about the data-generation process, with the aim of analysing those data and drawing inference from that analysis. Many statistical tasks are undertaken during this analysis; they include classification, forecasting, prediction and testing. Model-building has assumed substantial importance, as new technologies enable data on highly complex phenomena to be gathered in very large quantities. This creates a demand for more complex models, and requires the model-building process itself to be adaptive. The word “paradigm” refers to philosophies, frameworks and methodologies for developing and interpreting statistical models, in the context of data, and applying them for inference. In order to solve contemporary statistical problems it is often necessary to combine techniques from previously separate paradigms. The workshop addressed model-building paradigms that are at the frontiers of modern statistical research. It tried to create synergies, by delineating the connections and collisions among different paradigms. It also endeavoured to shape the future evolution of paradigms. http://publications.mfo.de/handle/mfo/3035 Harmonische Analysis und Darstellungstheorie Topologischer Gruppen This was a meeting in the general area of representation theory and harmonic analysis on reductive groups. Mon, 01 Jan 2007 00:00:00 GMT http://publications.mfo.de/handle/mfo/3035 2007-01-01T00:00:00Z This was a meeting in the general area of representation theory and harmonic analysis on reductive groups.