http://publications.mfo.de/handle/mfo/1404 Tue, 07 Apr 2026 23:54:55 GMT 2026-04-07T23:54:55Z http://publications.mfo.de/handle/mfo/4125 Curvatura escalar positiva y aplicaciones Rosenberg, Jonathan; Wraith, David Introducimos la idea de curvatura, incluyendo su desarrollo histórico, y nos enfocamos en la curvatura escalar de una variedad. Uno de los temas principales de investigación actual es entender la curvatura escalar positiva. Discutiremos por qué es interesante y su relación con la teoría general de la relatividad. Fri, 01 Jan 2021 00:00:00 GMT http://publications.mfo.de/handle/mfo/4125 2021-01-01T00:00:00Z Rosenberg, Jonathan Wraith, David Introducimos la idea de curvatura, incluyendo su desarrollo histórico, y nos enfocamos en la curvatura escalar de una variedad. Uno de los temas principales de investigación actual es entender la curvatura escalar positiva. Discutiremos por qué es interesante y su relación con la teoría general de la relatividad. http://publications.mfo.de/handle/mfo/3693 Is it possible to predict the far future before the near future is known accurately? Gander, Martin J. It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict the future. However, to make accurate predictions can require extremely large amounts of computation. If we need seven days to compute a prediction for the weather tomorrow and the day after tomorrow, the prediction arrives too late and is thus not a prediction any more. Although it may seem improbable, with the advent of powerful computers with many parallel processors, it is possible to compute a prediction for tomorrow and the day after tomorrow simultaneously. We describe a mathematical algorithm which is designed to achieve this. Wed, 18 Dec 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3693 2019-12-18T00:00:00Z Gander, Martin J. It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict the future. However, to make accurate predictions can require extremely large amounts of computation. If we need seven days to compute a prediction for the weather tomorrow and the day after tomorrow, the prediction arrives too late and is thus not a prediction any more. Although it may seem improbable, with the advent of powerful computers with many parallel processors, it is possible to compute a prediction for tomorrow and the day after tomorrow simultaneously. We describe a mathematical algorithm which is designed to achieve this. http://publications.mfo.de/handle/mfo/3692 The Interaction of Curvature and Topology Kordaß, Jan-Bernhard In this snapshot we will outline the mathematical notion of curvature by means of comparison geometry. We will then try to address questions as the ways in which curvature might influence the topology of a space, and vice versa. Wed, 18 Dec 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3692 2019-12-18T00:00:00Z Kordaß, Jan-Bernhard In this snapshot we will outline the mathematical notion of curvature by means of comparison geometry. We will then try to address questions as the ways in which curvature might influence the topology of a space, and vice versa. http://publications.mfo.de/handle/mfo/3691 The Mathematics of Fluids and Solids Kaltenbacher, Barbara; Kukavica, Igor; Lasiecka, Irena; Triggiani, Roberto; Tuffaha, Amjad; Webster, Justin Fluid-structure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a sample of the most significant questions that mathematicians try to answer. Wed, 18 Dec 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3691 2019-12-18T00:00:00Z Kaltenbacher, Barbara Kukavica, Igor Lasiecka, Irena Triggiani, Roberto Tuffaha, Amjad Webster, Justin Fluid-structure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a sample of the most significant questions that mathematicians try to answer. http://publications.mfo.de/handle/mfo/3690 A surprising connection between quantum mechanics and shallow water waves Fillman, Jake; VandenBoom, Tom We describe a connection between quantum mechanics and nonlinear wave equations and highlight a few problems at the forefront of modern research in the intersection of these areas. Wed, 11 Dec 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3690 2019-12-11T00:00:00Z Fillman, Jake VandenBoom, Tom We describe a connection between quantum mechanics and nonlinear wave equations and highlight a few problems at the forefront of modern research in the intersection of these areas. http://publications.mfo.de/handle/mfo/3689 Formation Control and Rigidity Theory Zelazo, Daniel; Zhao, Shiyu Formation control is one of the fundamental coordination tasks for teams of autonomous vehicles. Autonomous formations are used in applications ranging from search-and-rescue operations to deep space exploration, with benefits including increased robustness to failures and risk mitigation for human operators. The challenge of formation control is to develop distributed control strategies using vehicle onboard sensing that ensures the desired formation is obtained. This snapshot describes how the mathematical theory of rigidity has emerged as an important tool in the study of formation control problems. Wed, 11 Dec 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3689 2019-12-11T00:00:00Z Zelazo, Daniel Zhao, Shiyu Formation control is one of the fundamental coordination tasks for teams of autonomous vehicles. Autonomous formations are used in applications ranging from search-and-rescue operations to deep space exploration, with benefits including increased robustness to failures and risk mitigation for human operators. The challenge of formation control is to develop distributed control strategies using vehicle onboard sensing that ensures the desired formation is obtained. This snapshot describes how the mathematical theory of rigidity has emerged as an important tool in the study of formation control problems. http://publications.mfo.de/handle/mfo/3687 Expander graphs and where to find them Khukhro, Ana Graphs are mathematical objects composed of a collection of “dots” called vertices, some of which are joined by lines called edges. Graphs are ideal for visually representing relations between things, and mathematical properties of graphs can provide an insight into real-life phenomena. One interesting property is how connected a graph is, in the sense of how easy it is to move between the vertices along the edges. The topic dealt with here is the construction of particularly well-connected graphs, and whether or not such graphs can happily exist in worlds similar to ours. Fri, 22 Nov 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3687 2019-11-22T00:00:00Z Khukhro, Ana Graphs are mathematical objects composed of a collection of “dots” called vertices, some of which are joined by lines called edges. Graphs are ideal for visually representing relations between things, and mathematical properties of graphs can provide an insight into real-life phenomena. One interesting property is how connected a graph is, in the sense of how easy it is to move between the vertices along the edges. The topic dealt with here is the construction of particularly well-connected graphs, and whether or not such graphs can happily exist in worlds similar to ours. http://publications.mfo.de/handle/mfo/3686 Deep Learning and Inverse Problems Arridge, Simon; de Hoop, Maarten; Maass, Peter; Öktem, Ozan; Schönlieb, Carola; Unser, Michael Big data and deep learning are modern buzz words which presently infiltrate all fields of science and technology. These new concepts are impressive in terms of the stunning results they achieve for a large variety of applications. However, the theoretical justification for their success is still very limited. In this snapshot, we highlight some of the very recent mathematical results that are the beginnings of a solid theoretical foundation for the subject. Thu, 21 Nov 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3686 2019-11-21T00:00:00Z Arridge, Simon de Hoop, Maarten Maass, Peter Öktem, Ozan Schönlieb, Carola Unser, Michael Big data and deep learning are modern buzz words which presently infiltrate all fields of science and technology. These new concepts are impressive in terms of the stunning results they achieve for a large variety of applications. However, the theoretical justification for their success is still very limited. In this snapshot, we highlight some of the very recent mathematical results that are the beginnings of a solid theoretical foundation for the subject. http://publications.mfo.de/handle/mfo/3688 Mixed-dimensional models for real-world applications Nordbotten, Jan Martin We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixed-dimensional models. We first give several examples, and then an overview of recent progress made towards finding a general method of solution of such problems. Thu, 21 Nov 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3688 2019-11-21T00:00:00Z Nordbotten, Jan Martin We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixed-dimensional models. We first give several examples, and then an overview of recent progress made towards finding a general method of solution of such problems. http://publications.mfo.de/handle/mfo/3685 Touching the transcendentals: tractional motion from the bir th of calculus to future perspectives Milici, Pietro When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century but today, mainstream conception relegates geometry to be merely a tool of visualization. In this snapshot, however, we consider geometric and constructive components of calculus. We reinterpret “tractional motion”, a late 17th century method to draw transcendental curves, in order to reintroduce “ideal machines” in math foundation for a constructive approach to calculus that avoids the concept of infinity. Thu, 21 Nov 2019 00:00:00 GMT http://publications.mfo.de/handle/mfo/3685 2019-11-21T00:00:00Z Milici, Pietro When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century but today, mainstream conception relegates geometry to be merely a tool of visualization. In this snapshot, however, we consider geometric and constructive components of calculus. We reinterpret “tractional motion”, a late 17th century method to draw transcendental curves, in order to reintroduce “ideal machines” in math foundation for a constructive approach to calculus that avoids the concept of infinity.