http://publications.mfo.de/handle/mfo/1294 Tue, 07 Apr 2026 06:24:07 GMT 2026-04-07T06:24:07Z http://publications.mfo.de/handle/mfo/4124 Espacios de métricas Riemannianas Bustamante, Mauricio; Kordaß, Jan-Bernhard Las métricas riemannianas dan a las variedades suaves, como las superficies, propiedades geométricas intrínsecas, por ejemplo la curvatura. También permiten medir cantidades como distancias, ángulos y volúmenes. Estas son las nociones que utilizamos para caracterizar la "forma'' de una variedad. El espacio de métricas riemannianas de una variedad suave es un objeto matemático que codifica las posibles maneras en las que podemos deformar geométricamente la forma de la variedad. Fri, 01 Jan 2021 00:00:00 GMT http://publications.mfo.de/handle/mfo/4124 2021-01-01T00:00:00Z Bustamante, Mauricio Kordaß, Jan-Bernhard Las métricas riemannianas dan a las variedades suaves, como las superficies, propiedades geométricas intrínsecas, por ejemplo la curvatura. También permiten medir cantidades como distancias, ángulos y volúmenes. Estas son las nociones que utilizamos para caracterizar la "forma'' de una variedad. El espacio de métricas riemannianas de una variedad suave es un objeto matemático que codifica las posibles maneras en las que podemos deformar geométricamente la forma de la variedad. http://publications.mfo.de/handle/mfo/1355 Computing the long term evolution of the solar system with geometric numerical integrators Fiorelli Vilmart, Shaula; Vilmart, Gilles Simulating the dynamics of the Sun–Earth–Moon system with a standard algorithm yields a dramatically wrong solution, predicting that the Moon is ejected from its orbit. In contrast, a well chosen algorithm with the same initial data yields the correct behavior. We explain the main ideas of how the evolution of the solar system can be computed over long times by taking advantage of so-called geometric numerical methods. Short sample codes are provided for the Sun–Earth–Moon system. Wed, 27 Dec 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1355 2017-12-27T00:00:00Z Fiorelli Vilmart, Shaula Vilmart, Gilles Simulating the dynamics of the Sun–Earth–Moon system with a standard algorithm yields a dramatically wrong solution, predicting that the Moon is ejected from its orbit. In contrast, a well chosen algorithm with the same initial data yields the correct behavior. We explain the main ideas of how the evolution of the solar system can be computed over long times by taking advantage of so-called geometric numerical methods. Short sample codes are provided for the Sun–Earth–Moon system. http://publications.mfo.de/handle/mfo/1352 Spaces of Riemannian metrics Bustamante, Mauricio; Kordaß, Jan-Bernhard Riemannian metrics endow smooth manifolds such as surfaces with intrinsic geometric properties, for example with curvature. They also allow us to measure quantities like distances, angles and volumes. These are the notions we use to characterize the "shape" of a manifold. The space of Riemannian metrics is a mathematical object that encodes the many possible ways in which we can geometrically deform the shape of a manifold.; [Also available in Spanish] Thu, 28 Dec 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1352 2017-12-28T00:00:00Z Bustamante, Mauricio Kordaß, Jan-Bernhard Riemannian metrics endow smooth manifolds such as surfaces with intrinsic geometric properties, for example with curvature. They also allow us to measure quantities like distances, angles and volumes. These are the notions we use to characterize the "shape" of a manifold. The space of Riemannian metrics is a mathematical object that encodes the many possible ways in which we can geometrically deform the shape of a manifold. [Also available in Spanish] http://publications.mfo.de/handle/mfo/1351 Mathematics plays a key role in scientific computing Shu, Chi-Wang I attended a very interesting workshop at the research center MFO in Oberwolfach on “Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws”. The title sounds a bit technical, but in plain language we could say: The theme is to survey recent research concerning how mathematics is used to study numerical algorithms involving a special class of equations. These equations arise from computer simulations to solve application problems including those in aerospace engineering, automobile design, and electromagnetic waves in communications as examples. This topic belongs to the general research area called “scientific computing”. Fri, 29 Dec 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1351 2017-12-29T00:00:00Z Shu, Chi-Wang I attended a very interesting workshop at the research center MFO in Oberwolfach on “Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws”. The title sounds a bit technical, but in plain language we could say: The theme is to survey recent research concerning how mathematics is used to study numerical algorithms involving a special class of equations. These equations arise from computer simulations to solve application problems including those in aerospace engineering, automobile design, and electromagnetic waves in communications as examples. This topic belongs to the general research area called “scientific computing”. http://publications.mfo.de/handle/mfo/1335 Solving quadratic equations in many variables Tignol, Jean-Pierre Fields are number systems in which every linear equation has a solution, such as the set of all rational numbers $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. All fields have the same properties in relation with systems of linear equations, but quadratic equations behave differently from field to field. Is there a field in which every quadratic equation in five variables has a solution, but some quadratic equation in four variables has no solution? The answer is in this snapshot. Sat, 30 Dec 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1335 2017-12-30T00:00:00Z Tignol, Jean-Pierre Fields are number systems in which every linear equation has a solution, such as the set of all rational numbers $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. All fields have the same properties in relation with systems of linear equations, but quadratic equations behave differently from field to field. Is there a field in which every quadratic equation in five variables has a solution, but some quadratic equation in four variables has no solution? The answer is in this snapshot. http://publications.mfo.de/handle/mfo/1332 Computational Optimal Transport Solomon, Justin Optimal transport is the mathematical discipline of matching supply to demand while minimizing shipping costs. This matching problem becomes extremely challenging as the quantity of supply and demand points increases; modern applications must cope with thousands or millions of these at a time. Here, we introduce the computational optimal transport problem and summarize recent ideas for achieving new heights in efficiency and scalability. Thu, 21 Dec 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1332 2017-12-21T00:00:00Z Solomon, Justin Optimal transport is the mathematical discipline of matching supply to demand while minimizing shipping costs. This matching problem becomes extremely challenging as the quantity of supply and demand points increases; modern applications must cope with thousands or millions of these at a time. Here, we introduce the computational optimal transport problem and summarize recent ideas for achieving new heights in efficiency and scalability. http://publications.mfo.de/handle/mfo/1329 A few shades of interpolation Szpond, Justyna The topic of this snapshot is interpolation. In the ordinary sense, interpolation means to insert something of a different nature into something else. In mathematics, interpolation means constructing new data points from given data points. The new points usually lie in between the already-known points. The purpose of this snapshot is to introduce a particular type of interpolation, namely, polynomial interpolation. This will be explained starting from basic ideas that go back to the ancient Babylonians and Greeks, and will arrive at subjects of current research activity. Thu, 07 Dec 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1329 2017-12-07T00:00:00Z Szpond, Justyna The topic of this snapshot is interpolation. In the ordinary sense, interpolation means to insert something of a different nature into something else. In mathematics, interpolation means constructing new data points from given data points. The new points usually lie in between the already-known points. The purpose of this snapshot is to introduce a particular type of interpolation, namely, polynomial interpolation. This will be explained starting from basic ideas that go back to the ancient Babylonians and Greeks, and will arrive at subjects of current research activity. http://publications.mfo.de/handle/mfo/1328 Closed geodesics on surfaces and Riemannian manifolds Radeschi, Marco Geodesics are special paths in surfaces and so-called Riemannian manifolds which connect close points in the shortest way. Closed geodesics are geodesics which go back to where they started. In this snapshot we talk about these special paths, and the efforts to find closed geodesics. Thu, 07 Dec 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1328 2017-12-07T00:00:00Z Radeschi, Marco Geodesics are special paths in surfaces and so-called Riemannian manifolds which connect close points in the shortest way. Closed geodesics are geodesics which go back to where they started. In this snapshot we talk about these special paths, and the efforts to find closed geodesics. http://publications.mfo.de/handle/mfo/1313 Molecular Quantum Dynamics Hagedorn, George A.; Lasser, Caroline We provide a brief introduction to some basic ideas of Molecular Quantum Dynamics. We discuss the scope, strengths and main applications of this field of science. Finally, we also mention open problems of current interest in this exciting subject. Tue, 24 Oct 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1313 2017-10-24T00:00:00Z Hagedorn, George A. Lasser, Caroline We provide a brief introduction to some basic ideas of Molecular Quantum Dynamics. We discuss the scope, strengths and main applications of this field of science. Finally, we also mention open problems of current interest in this exciting subject. http://publications.mfo.de/handle/mfo/1311 Mathematische Modellierung von Krebswachstum Engwer, Christian; Knappitsch, Markus Krebs ist eine der größten Herausforderungen der modernen Medizin. Der WHO zufolge starben 2012 weltweit 8,2 Millionen Menschen an Krebs. Bis heute sind dessen molekulare Mechanismen nur in Teilen verstanden, was eine erfolgreiche Behandlung erschwert. Mathematische Modellierung und Computersimulationen können helfen, die Mechanismen des Tumorwachstums besser zu verstehen. Sie eröffnen somit neue Chancen für zukünftige Behandlungsmethoden. In diesem Schnappschuss steht die mathematische Modellierung von Glioblastomen im Fokus, einer Klasse sehr agressiver Tumore im menschlichen Gehirn. Tue, 17 Oct 2017 00:00:00 GMT http://publications.mfo.de/handle/mfo/1311 2017-10-17T00:00:00Z Engwer, Christian Knappitsch, Markus Krebs ist eine der größten Herausforderungen der modernen Medizin. Der WHO zufolge starben 2012 weltweit 8,2 Millionen Menschen an Krebs. Bis heute sind dessen molekulare Mechanismen nur in Teilen verstanden, was eine erfolgreiche Behandlung erschwert. Mathematische Modellierung und Computersimulationen können helfen, die Mechanismen des Tumorwachstums besser zu verstehen. Sie eröffnen somit neue Chancen für zukünftige Behandlungsmethoden. In diesem Schnappschuss steht die mathematische Modellierung von Glioblastomen im Fokus, einer Klasse sehr agressiver Tumore im menschlichen Gehirn.