Now showing items 11-20 of 21
Configuration spaces and braid groups
[SNAP-2019-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-10-08)
In this snapshot we introduce configuration spaces and explain how a mathematician studies their ‘shape’. This will lead us to consider paths of configurations and braid groups, and to explore how algebraic properties of ...
Touching the transcendentals: tractional motion from the bir th of calculus to future perspectives
[SNAP-2019-013-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
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 ...
Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)
[SNAP-2019-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
Throughout the history of dynamical systems, instruments have been used to calculate and visualize (approximate) solutions of differential equations. Here we describe the approach of a group of physicists and engineers ...
Expander graphs and where to find them
[SNAP-2019-016-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-22)
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 ...
Formation Control and Rigidity Theory
[SNAP-2019-017-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-11)
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 ...
A surprising connection between quantum mechanics and shallow water waves
[SNAP-2019-018-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-11)
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.
Deep Learning and Inverse Problems
[SNAP-2019-015-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
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 ...
Mixed-dimensional models for real-world applications
[SNAP-2019-014-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
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 ...
The Interaction of Curvature and Topology
[SNAP-2019-020-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)
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 ...
Is it possible to predict the far future before the near future is known accurately?
[SNAP-2019-021-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)
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 ...