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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 ...
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 ...
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.
Mixed volumes and mixed integrals
[SNAP-2018-014-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-29)
In recent years, mathematicians have developed new
approaches to study convex sets: instead of considering
convex sets themselves, they explore certain functions
or measures that are related to them. Problems
from ...
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 ...
Number theory in quantum computing
[SNAP-2018-012-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-07)
Algorithms are mathematical procedures developed
to solve a problem. When encoded on a computer,
algorithms must be "translated" to a series of simple
steps, each of which the computer knows how
to do. This task is ...
Topological Complexity, Robotics and Social Choice
[SNAP-2018-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-10)
Topological complexity is a number that measures
how hard it is to plan motions (for robots, say) in
terms of a particular space associated to the kind of
motion to be planned. This is a burgeoning subject
within the ...
Data assimilation: mathematics for merging models and data
[SNAP-2018-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-10)
When you describe a physical process, for example,
the weather on Earth, or an engineered system, such
as a self-driving car, you typically have two sources of
information. The first is a mathematical model, and
the ...
Tropical geometry
[SNAP-2018-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-19)
What kind of strange spaces hide behind the enigmatic
name of tropical geometry? In the tropics, just
as in other geometries, one of the simplest objects is
a line. Therefore, we begin our exploration by considering
tropical ...