2  Snapshots of modern mathematics from Oberwolfach
Snapshots of modern mathematics from Oberwolfach explain mathematical problems and ideas in an accessible and understandable way. They provide exciting insights into current topics of the mathematical community for everyone who is interested in modern mathematics.
The snapshots are written by participants of the scientific program at the MFO, who volunteer to explain an important aspect of their research. A team of editors assists them in communicating complicated matters to a broad audience. The MFO publishes the snapshots for free download under a Creative Commons license here and on the IMAGINARY platform.
The Snapshot project is designed to promote the understanding and appreciation of modern mathematics and mathematical research in the general public worldwide. The targeted readership consists of mathematics teachers, science journalists, undergraduate and advanced high school students. If you are interested in writing a snapshot, please contact the organizers of the program in which you are participating.
The project started in January 2014 as part of the project "Oberwolfach meets IMAGINARY". It is funded by the Klaus Tschira Foundation and has also been supported by the Oberwolfach Foundation and the MFO.
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Computing the long term evolution of the solar system with geometric numerical integrators
[SNAP2017009EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171227)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 ... 
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 ... 
Spaces of Riemannian metrics
[SNAP2017010EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171228)Riemannian metrics endow smooth manifolds such as surfaces with intrinsic geometric properties, for example with curvature. They also allow us to measure quantities like distances, angles and volumes. These are the ... 
Mathematics plays a key role in scientific computing
[SNAP2017011EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171229)I attended a very interesting workshop at the research center MFO in Oberwolfach on “Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws”. The title sounds a bit technical, but in plain language ... 
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 ... 
Solving quadratic equations in many variables
[SNAP2017012EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171230)Fields are number systems in which every linear equation has a solution, such as the set of all rational numbers $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. All fields have the same properties in relation ... 
Computational Optimal Transport
[SNAP2017008EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171221)Optimal transport is the mathematical discipline of matching supply to demand while minimizing shipping costs. This matching problem becomes extremely challenging as the quantity of supply and demand points increases; ... 
A few shades of interpolation
[SNAP2017007EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171207)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 ... 
Closed geodesics on surfaces and Riemannian manifolds
[SNAP2017005EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171207)Geodesics are special paths in surfaces and socalled Riemannian manifolds which connect close points in the shortest way. Closed geodesics are geodesics which go back to where they started. In this snapshot we talk ... 
Molecular Quantum Dynamics
[SNAP2017006EN] (Mathematisches Forschungsinstitut Oberwolfach, 20171024)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 ... 
Mathematische Modellierung von Krebswachstum
[SNAP2017004DE] (Mathematisches Forschungsinstitut Oberwolfach, 20171017)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 ... 
Aperiodic Order and Spectral Properties
[SNAP2017003EN] (Mathematisches Forschungsinstitut Oberwolfach, 20170914)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 ... 
Winkeltreue zahlt sich aus
[SNAP2017001DE] (Mathematisches Forschungsinstitut Oberwolfach, 20170823)Nicht nur Seefahrerinnen, auch Computergrafikerinnen und Physikerinnen wissen Winkeltreue zu schätzen. Doch beschränkte Rechenkapazitäten und Vereinfachungen in theoretischen Modellen erfordern es, winkeltreue Abbildungen ... 
News on quadratic polynomials
[SNAP2017002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20170718)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 ... 
Towards a Mathematical Theory of Turbulence in Fluids
[SNAP2016015EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Fluid mechanics is the theory of how liquids and gases move around. For the most part, the basic physics are well understood and the mathematical models look relatively simple. Despite this, fluids display a dazzling mystery ... 
Profinite groups
[SNAP2016014EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Profinite objects are mathematical constructions used to collect, in a uniform manner, facts about infinitely many finite objects. We shall review recent progress in the theory of profinite groups, due to Nikolov and Segal, ... 
The adaptive finite element method
[SNAP2016013EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Computer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other ... 
Footballs and donuts in four dimensions
[SNAP2016012EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world ...