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Now showing items 21-30 of 161
Friezes and tilings
[SNAP-2015-004-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
Friezes have occured as architectural ornaments for many centuries. In this snapshot, we consider the mathematical analogue of friezes as introduced in the 1970s by Conway and Coxeter. Recently, infinite versions of such ...
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 ...
Operator theory and the singular value decomposition
[SNAP-2014-009-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
This is a snapshot about operator theory and one of its fundamental tools: the singular value decomposition (SVD). The SVD breaks up linear transformations into simpler mappings, thus unveiling their geometric properties. ...
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 ...
From Betti numbers to ℓ²-Betti numbers
[SNAP-2020-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-15)
We provide a leisurely introduction to ℓ²-Betti numbers,
which are topological invariants, by relating
them to their much older cousins, Betti numbers. In
the end we present an open research problem about
ℓ²-Betti numbers.
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 ...
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 ...
Modeling communication and movement: from cells to animals and humans
[SNAP-2015-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
Communication forms the basis of biological interactions. While the use of a single communication mechanism (for example visual communication) by a species is quite well understood, in nature the majority of species ...
Special values of zeta functions and areas of triangles
[SNAP-2015-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
In this snapshot we give a glimpse of the interplay of special values of zeta functions and volumes of triangles. Special values of zeta functions and their generalizations arise in the computation of volumes of moduli ...
Biological shape analysis with geometric statistics and learning
[SNAP-2022-008-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)
The advances in biomedical imaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, shape data may hold ...