2018
2018
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Mixed volumes and mixed integrals
[SNAP2018014EN] (Mathematisches Forschungsinstitut Oberwolfach, 20181229)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 ... 
Estimating the volume of a convex body
[SNAP2018015EN] (Mathematisches Forschungsinstitut Oberwolfach, 20181230)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. 
Topological Complexity, Robotics and Social Choice
[SNAP2018005EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180810)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 ... 
A short story on optimal transport and its many applications
[SNAP2018013EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180808)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
[SNAP2018012EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180807)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 ... 
Tropical geometry
[SNAP2018007EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180719)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 ... 
Data assimilation: mathematics for merging models and data
[SNAP2018011EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180710)When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a selfdriving car, you typically have two sources of information. The first is a mathematical model, and the ... 
Fast Solvers for Highly Oscillatory Problems
[SNAP2018006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180626)Waves of diverse types surround us. Sound, light and other waves, such as microwaves, are crucial for speech, mobile phones, and other communication technologies. Elastic waves propagating through the Earth bounce ... 
Geometry behind one of the Painlevé III differential equations
[SNAP2018010EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180620)The Painlevé equations are second order differential equations, which were first studied more than 100 years ago. Nowadays they arise in many areas in mathematics and mathematical physics. This snapshot discusses the ... 
The codimension
[SNAP2018009EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180619)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. 
The mathematics of aquatic locomotion
[SNAP2018008EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180619)Aquatic locomotion is a selfpropelled 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 ... 
Computing with symmetries
[SNAP2018003EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180306)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. 
Topological recursion
[SNAP2018002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180305)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
[SNAP2018004EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180306)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
[SNAP2018001EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180227)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 ...