Now showing items 2-12 of 12

• #### Closed geodesics on surfaces and Riemannian manifolds ﻿

[SNAP-2017-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-07)
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 ...
• #### Computational Optimal Transport ﻿

[SNAP-2017-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-21)
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; ...
• #### Computing the long term evolution of the solar system with geometric numerical integrators ﻿

[SNAP-2017-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-27)
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 ...
• #### A few shades of interpolation ﻿

[SNAP-2017-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-07)
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 ...
• #### Mathematics plays a key role in scientific computing ﻿

[SNAP-2017-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-29)
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 ...
• #### Mathematische Modellierung von Krebswachstum ﻿

[SNAP-2017-004-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-17)
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 ...
• #### Molecular Quantum Dynamics ﻿

[SNAP-2017-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-24)
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 ...
• #### News on quadratic polynomials ﻿

[SNAP-2017-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-18)
Many problems in mathematics have remained unsolved because of missing links between mathematical disciplines, such as algebra, geometry, analysis, or number theory. Here we introduce a recently discovered result concerning ...
• #### Solving quadratic equations in many variables ﻿

[SNAP-2017-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-30)
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 ...
• #### Spaces of Riemannian metrics ﻿

[SNAP-2017-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-28)
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 ...
• #### Winkeltreue zahlt sich aus ﻿

[SNAP-2017-001-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2017-08-23)
Nicht nur Seefahrerinnen, auch Computergrafikerinnen und Physikerinnen wissen Winkeltreue zu schätzen. Doch beschränkte Rechenkapazitäten und Vereinfachungen in theoretischen Modellen erfordern es, winkeltreue Abbildungen ...