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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 ...
Swallowtail on the shore
[SNAP-2014-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
Platonic solids, Felix Klein, H.S.M. Coxeter and a flap of a swallowtail: The five Platonic solids tetrahedron, cube, octahedron, icosahedron and dodecahedron have always attracted much curiosity from mathematicians, not ...
On the containment problem
[SNAP-2016-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)
Mathematicians routinely speak two languages: the language of geometry and the language of algebra. When translating between these languages, curves and lines become sets of polynomials called “ideals”. Often there are ...
Searching for the monster in the trees
[SNAP-2022-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-04-13)
The Monster finite simple group is almost unimaginably large, with about 8 × 1053 elements in it. Trying to understand such an immense object requires both theory and computer programs. In this snapshot, we discuss finite ...
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 ...
A short story on optimal transport and its many applications
[SNAP-2018-013-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-08)
We present some examples of optimal transport problems
and of applications to different sciences (logistics,
economics, image processing, and a little bit of
evolution equations) through the crazy story of an
industrial ...
From the dollar game to the Riemann-Roch Theorem
[SNAP-2021-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2021-02-23)
What is the dollar game? What can you do to win
it? Can you always win it? In this snapshot you
will find answers to these questions as well as several
of the mathematical surprises that lurk in the background,
including ...
Modelling the spread of brain tumours
[SNAP-2015-013-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
The study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment ...
Statistics and dynamical phenomena
[SNAP-2014-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2014)
A friend of mine, an expert in statistical genomics, told me the following story: At a dinner party, an attractive lady asked him, "What do you do for a living?" He replied, "I model." As my friend is a handsome man, the ...
Limits of graph sequences
[SNAP-2019-010-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)
Graphs are simple mathematical structures used to
model a wide variety of real-life objects. With the
rise of computers, the size of the graphs used for
these models has grown enormously. The need to efficiently
represent ...