Now showing items 41-60 of 109

• #### Polyhedra and commensurability ﻿

[SNAP-2016-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
This snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it ...
• #### Wie steuert man einen Kran? ﻿

[SNAP-2016-007-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
Die Steuerung einer Last an einem Kran ist ein technisch und mathematisch schwieriges Problem, da die Bewegung der Last nur indirekt beeinflusst werden kann. Anhand eines Masse-Feder-Systems illustrieren wir diese ...
• #### 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 ...
• #### 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 ...
• #### Aperiodic Order and Spectral Properties ﻿

[SNAP-2017-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2017-09-14)
Periodic structures like a typical tiled kitchen floor or the arrangement of carbon atoms in a diamond crystal certainly possess a high degree of order. But what is order without periodicity? In this snapshot, we are ...
• #### 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 ...
• #### 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 ...
• #### 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 ...
• #### Spaces of Riemannian metrics ﻿

[SNAP-2017-010-ENSNAP-2017-010-ES] (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 ...
• #### 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 ...
• #### 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 ...
• #### The Algebraic Statistics of an Oberwolfach Workshop ﻿

[SNAP-2018-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-02-27)
Algebraic Statistics builds on the idea that statistical models can be understood via polynomials. Many statistical models are parameterized by polynomials in the model parameters; others are described implicitly by ...
• #### Topological recursion ﻿

[SNAP-2018-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-05)
In this snapshot we present the concept of topological recursion – a new, surprisingly powerful formalism at the border of mathematics and physics, which has been actively developed within the last decade. After introducing ...
• #### Prony’s method: an old trick for new problems ﻿

[SNAP-2018-004-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-06)
In 1795, French mathematician Gaspard de Prony invented an ingenious trick to solve a recovery problem, aiming at reconstructing functions from their values at given points, which arose from a specific application in ...
• #### Computing with symmetries ﻿

[SNAP-2018-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-06)
Group theory is the study of symmetry, and has many applications both within and outside mathematics. In this snapshot, we give a brief introduction to symmetries, and how to compute with them.
• #### The mathematics of aquatic locomotion ﻿

[SNAP-2018-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-19)
Aquatic locomotion is a self-propelled motion through a liquid medium. It can be of biological nature (fish, microorganisms,. . .) or performed by robotic swimmers. This snapshot aims to introduce the reader to some ...
• #### The codimension ﻿

[SNAP-2018-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-19)
In this snapshot we discuss the notion of codimension, which is, in a sense, “dual” to the notion of dimension and is useful when studying the relative position of one object insider another one.