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Now showing items 81-90 of 161
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 ...
Darcy's law and groundwater flow modelling
[SNAP-2015-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
Formulations of natural phenomena are derived, sometimes, from experimentation and observation. Mathematical methods can be applied to expand on these formulations, and develop them into better models. In the year 1856, ...
Quantum symmetry
[SNAP-2020-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2020-06-04)
In mathematics, symmetry is usually captured using
the formalism of groups. However, the developments
of the past few decades revealed the need to go beyond
groups: to “quantum groups”. We explain the
passage from ...
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 ...
Random permutations
[SNAP-2019-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-12)
100 people leave their hats at the door at a party and
pick up a completely random hat when they leave.
How likely is it that at least one of them will get
back their own hat? If the hats carry name tags,
how difficult ...
The mystery of sleeping sickness – why does it keep waking up?
[SNAP-2015-015-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about ...
Estimating the volume of a convex body
[SNAP-2018-015-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-30)
Sometimes the volume of a convex body needs to
be estimated, if we cannot calculate it analytically.
We explain how statistics can be used not only to
approximate the volume of the convex body, but also
its shape.
Ultrafilter methods in combinatorics
[SNAP-2021-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2021-06-25)
Given a set X, ultrafilters determine which subsets
of X should be considered as large. We illustrate
the use of ultrafilter methods in combinatorics by
discussing two cornerstone results in Ramsey theory,
namely ...
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.
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 ...